PRINCIPLES 


PRACTICE 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

SCHOOL  OF  LAW 
GIFT  OF 

Walter  ?.r.  Atkinson 
Dell  L.  Falls 

C.  Douglas  Fikle 
Of  class  of 


A  TREATISE 


PRINCIPLES   AND   PRACTICE 


LIFE    INSURANCE: 


BEING  AN  ARITHMETICAL  EXPLANATION  OF  THE  COMPUTATIONS 

INVOLVED  IN  THE  SCIENCE  OF  LlFE  CONTINGENCIES, 

TO  WHICH  ARE  ADDED 


VALUABLE  TABLES  FOR  REFERENCE. 


BY  NATHAN  WILLEY,  ACTUARY. 


NEW  YORK: 

Offices  O/THE  SPECTATOR, 

J.  H.  AND  C.  M.  GOODSELL,  PUBLISHERS. 

1872. 


'Entered   according  to  Act  of  Congress,  in  the  year   1873,  by 

J.    H.   AND   C.    M.    GOODSELL, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


THE  SPECTATOR  PRESS, 

J.  H.  AND   C.  M.  GOODSELL,  Proprietors, 

Nos.  93-95  Liberty  St.,  New  fork. 


k 


PREFACE. 

The  design  of  this  work  is  to  furnish  the  public  with  a 
means  of  clearly  understanding  the  fundamental  principles  of 
Life  Insurance,  and  to  enable  agents  to  present  them  in  a  concise 
and  forcible  manner.  To  accomplish  this  result,  the  author  has 
attempted  to  explain  the  mathematical  laws  which  the  study  and 
experience  of  the  past  two  centuries  have  shown  to  lie  at  the 
foundation  of  the  science.  In  this  undertaking  he  has  endeav- 
ored to  confine  himself  strictly  to  those  topics  which  the  experi- 
ence of  American  companies,  during  the  last  few  years,  has  shown 
to  be  absolutely  necessary  to  an  intelligent  and  successful  prose- 
cution of  the  business,  and  to  illustrate  them  in  such  a  manner 
that  they  may  be  comprehended  by  any  one  who  is  willing  to 
give  the  subject  a  careful  investigation.  Those  who  still  remain 
prejudiced  against  Life  Insurance  are  confirmed  in  their  opinions 
more  by  a  want  of  correct  information  than  by  any  solid  argu- 
ment which  they  can  produce  against  it,  and  the  sooner  it  is 
stripped  of  forbidden  technical  nomenclature  and  formulas, 
and  adapted  to  the  comprehension  of  the  average  intellect  of 
business  men,  the  greater  will  be  the  popular  appreciation  of  its. 
merits.  Both  officers  and  agents  of  companies  should  be  able  to- 
meet  any  objections  raised  against  Life  Insurance,  and  to  explain 
its  principles  so  clearly  that  the  public  may  see  that  it  is  a  plain 
financial  transaction,  giving  support  to  the  families  of  thousands 
of  claimants  every  year,  and  throwing  its  mantle  of  protec- 
tion around  nearly  a  million  of  its  living  patrons. 


CONTENTS. 


PAGE. 

Preface 3 

Definitions 1 1 

Interest  and  Discount 16 

Compound  Interest 16 

Annuities  certain  at  Compound  Interest 19 

Present  Values  and  Discount 21 

Deferred  Annuities 23 

Monetary  Tables,    4  per  cent 24 

4X     "       25 

5  "       

6  "       

.7        "       

8        " 

"  9        "      

10        "       

Life  Contingencies 

Tables  of  Mortality 33 

American  Experience  Table 33 

Combined  Experience  ;  or,  Actuaries  Table 34 

Rate  of  Interest 34 

Probability  of  Life 35 

Commutation  Columns 36 

Explanation  of  Life  Insurance 37 

Life  Annuities 43 

Valuation  of  Policies .  45 

Amount  at  Risk 47 

Cost  of  Insurance 48 

Distribution  of  Surplus 49 

Tontines  and  Tontine  Dividends 53 

Expectation  of  Life .  .      55 

Tables  of  Expectation  of  Life 56,  57 

Equation  of  Life 57 

Table  of  Equation  of  Life 58 


6  CONTENTS. 

FAGX 

Joint-Life  Policies 59 

Return-Premium  Plan 60 

Table  illustrating  Return  Premiums, 61 

Forfeiture  of  Policies  and  Paid-up  Insurance 62 

Surrender  Values 64 

Average  Duration  of  Policies 66 

American  Experience,  Mortality  Table 68 

Combined  Experience,                 "           69 

Commutation  Columns,  American  Experience,  4^  per  cent 70 

"                    Combined  Experience,  4  per  cent 72 

"                    American  Experience,  6  per  cent 74 

Net  Premiums,  American  Experience,  4^  Per  cent 76 

"                   Combined  Experience,  4  per  cent 77 

"  Term    Insurance,    American  Experience,    ^l/z    per 

cent 78 

"  Term    Insurance,    Combined    Experience,    4    per 

cent 78 

Explanation  of  Valuation  Tables   80 

Table  of  Comparative  Values  and  Ratios  of  Values 81 

Net  values,  Ordinary  Life  Policies,  American  Experience,  4^  per 

cent ' 82 

Net  values,  Ten-Payment  Life  Policies,  American  Experience,  4^ 

per  cent 84 

Net  values,  Ten-Year  Endowment  Policies,  American  Experience, 

4%  per  cent 86 

Net  values,  Fifteen-Year   Endowment   Policies,  American   Expe- 
rience, 4X  per  cent 88 

Net  values,  Twenty-Year  Endowment    Policies,  American  Expe- 
rience, 4%  per  cent 90 

Net  values,  Twenty-five  Year  Endowment  Policies,  American  Ex- 
perience, 4%  per  cent 92 

Net  values,  Thirty-Year  Endowment  Policies,  American  Experience 

4^  per  cent 94 

Net  values,  Thirty-five-Year  Endowment  Policies,  American  Expe- 
rience, AfYz  per  cent 96 

Combined  Experience  Table  of  Mortality 98 

Net  values,  Ordinary  Life  Policies,  Combined  Experience,  4  per 

cent 100 

Net  values,  Ten-Payment  Life  Policies,  Combined  Experience,  4  per 

cent 102 

Net  values,  Ten-Year  Endowment  Policies,  Combined  Experience, 

4  per  cent 104 

Net  values,  Fifteen-Year  Endowment  Policies,  Combined  Expe- 
rience, 4  per  cent 106 


CONTENTS.  7 

PAGK 

Net  values,  Twenty-Year  Endowment  Policies,  Combined  Expe- 
rience, 4  per  cent 108 

Net  values,  Twenty-five- Year  Endowment  Policies,  Combined  Ex- 
perience, 4  per  cent no 

Net   values,  Thirty-Year    Endowment    Policies,  Combined  Expe- 
rience, 4  per  cent 112 

Net  premiums,  Joint  Life  Policies,  Combined  Experience,  4  per 
cent , .  .    114 

Net  values,  Ordinary  Joint  Life  Policy,  Equal  ages,  4  per  cent 115 

"  "  "  Difference  in  ages  5  years. .    116 

"  "  "  "  10  years..    117 

"  "  "  "  i 5  years..    118 

Explanation  of  Cost  of  Insurance  Tables 1 20 

Cost  of  Insufance,  Ordinary  Life,  Single  Premium  Policy,  Ameri- 
can Experience,  4%  per  cent 121 

Cost  of  Insurance,   Ordinary  Life,  Single  Premium  Policy,  Com- 
bined Experience,  4  per  cent 121 

Cost  of  Insurance,  Ordinary  Life  Policy,  American  Experience,  4^ 
per  cent 122 

Cost  of  Insurance,  Ten-Payment  Life  Policy,  American  Experience, 
4J^  per  cent 123 

Cost  of  Insurance,  Ten-Year  Endowment  Policy,  American  Expe- 
rience, 4^  per  cent 1 24 

Cost  of  Insurance,  Fifteen- Year  Endowment  Policy,  American  Ex- 
perince,  4^  per  cent 125 

Cost  of    Insurance,  Twenty-Year   Endowment   Policy,  American 
Experience,  4^  per  cent 1 26 

Cost  of  Insurance,  Twenty-five-Year  Endowment  Policy,  Ameri- 
can Experience,  4^  per  cent 127 

Cost  of  Insurance,  Thirty-Year  Endowment  Policy,  American  Ex- 
perience, 4j^  per  cent 128 

Cost  of  Insurance,  Ordinary  Life   Policy,  Combined    Experience, 
4  per  cent 1 29 

Cost  of  Insurance,  Ten-Payment  Life  Policy,  Combined  Experience, 
4  per  cent 1 30 

Cost  of  Insurance,  Ten-Year   Endowment  Policy,  Combined  Ex- 
perience, 4  per  cent 131 

Cost  of  Insurance,  Fifteen-Year  Endowment  Policy,  Combined  Ex- 
perience, 4  per  cent 132 

Cost  of  Insurance,  Twenty-Year  Endowment    Policy,   Combined 
Experience,  4  per  cent 133 

Cost  of  Insurance,  Twenty-five-Year  Endowment  Policy,  Combined 
Experience,  4  per  cent 134 


8  CONTENTS. 

PAGE 

Cost  of  Insurance,  Thirty-Year  Endowment  Policy,  Combined  Ex- 
perience, 4  per  cent 135 

Net  Single  Premiums  applied  to  the  Massachusetts  Non-forfeiture 

Law,  Combined  Experience,  4  per  cent 136 

Insurance  due  on  Whole  Life  Policies,  according  to  the  Massachu- 
setts Non-forfeiture  Law 1 38 

Decimal  part  of  a  year  from  date  to  January  1st  following 140 

Life  Insurance  Formulae -142 

Formula  for  Annuities 143 

"         Whole  Life  Insurance 144 

"         Term  Insurance 144 

"         Endowment - .    144 

"         Endowment  Insurance • .   145 

"         Single  Premium,  Life • 146 

"         Annual  Premium,  Life 146 

"         Endowment  Insurance 146 

"         Joint  Life 146 

"         Return  Premium  Plan 147 

Valuation  of  Policies 148 

Prof.  Wright's  Accumulation  Formula. 1 50 

Fackler's  Formula 1 50 

McClintock's  Formula 1 50 

Romans'  Contribution  Formula 151 

Formula  for  Verifying  Commutation  Columns 151 

"  Equation  of  Life 151 

"  Expectation  of  Life 151 

Prof.  Wright's  Formula  for  Insurance  Values 151 

Prof.  Bartlett's  Formula  for  Surrender  Values 152 

Surrender  Values,  Table  of 155 

Valuation  of  Joint  Life  Policies.     By  Seth  C.  Chandler,  Jr 1 56 

Table  of. 1 57 

Valuation  of  Policies,  McClintock's  Method 158 

Table  of 160 

Valuation  Tables,  American  Experience,  4^  per  cent 168 

"  "  6  per  cent 173 

"  Combined  Experience,  4  per  cent 172 

Index 174 


DEFINITIONS   IN   LIFE   INSURANCE. 

Accumulation — The  annual  premiums  and  interest  during  the 
first  years  of  a  policy  are  largely  in  excess  of  the  annual  cost  of 
carrying  the  risk  ;  which  is  necessary  in  order  to  establish  a  fund 
to  pay  the  amount  insured  when  it  becomes  a  claim.  Hence, 
to  provide  for  the  payment  of  future  claims,  this  excess 
increases  by  compound  interest  and  additions  from  the  annual 
premium,  and  is  called  accumulation.  The  accumulation  for- 
mula expresses,  in  algebraic  language,  the  law  by  which  this 
increase  takes  place. 

Actuary — One  who  is  proficient  in  that  branch  of  life  insur- 
ance, which  is  strictly  of  a  scientific  and  mathematical  nature,  as 
the  preparation  of  tables  and  formulae,  calculation  of  policy  lia- 
bility, distribution  of  surplus,  etc. 

Annuity — A  sum  of  money  payable  at  regular  intervals.  An 
annuity  contingent  is  dependent  for  its  termination  upon  an  event 
which  may  or  will  occur,  as  the  death  of  the  annuitant  or  person 
who  receives  it. 

An  annuity  certain  is  a  sum  payable  during  a  definite  term  of 
years,  and  which  does  not  cease  in  the  meantime  in  the  event  of 
any  contingency.  The  interest  on  a  six  per  cent  bond  of  one 
thousand  dollars  is  an  annuity  certain  of  sixty  dollars  per  annum 
during  the  time  which  the  bond  has  to  run. 

A  perpetual  annuity  is  a  sum  of  money  payable  at  regular 
intervals  during  an  unlimited  seizes  of  years. 

A  deferred  annuity  is  one  in  which  the  regular  payments  are 
to  commence  at  some  future  period. 

A  joint  annuity  is  one  which  depends  upon  the  joint  existence 
of  two  or  more  lives  from  year  to  year. 

A  survivorship  annuity  is  one  which  continues  during  the  life- 
time of  the  survivor  of  two  or  more  lives. 

Assets — All  the  funds  and  available  property  of  any  kind 
belonging  to  a  company. 


12  PRINCIPLES  AND  PRACTICE 

Bonus — A  dividend  paid  to  policyholders  from  the  surplus 
of  a  company  over  and  above  the  liabilities.  "  Bonus  addition"  to 
a  policy  is  another  term  for  reversionary  insurance. 

Brokerage — A  commission  on  the  first  premiums  paid  to 
solicitors  of  life  insurance  companies  in  lieu  of  all  future  com- 
missions on  the  renewal  premiums. 

Commission — A  percentage  given  to  a  solicitor  or  agent  on 
premiums  collected  by  him. 

Commutation  Columns — Columns  formed  from  a  given  table  of 
mortality  and  rate  of  interest,  and  used  in  the  computation  of 
premium  rates  and  other  life  insurance  calculations. 

Company,  Insurance — A  number  of  persons  associated  to- 
gether for  the  purpose  of  effecting  insurance  against  risks  of  any 
kind.  A  stock  company  has  for  its  basis  a  capital  stock,  and  in- 
sures at  lower  premium  rates  than  those  of  mixed  or  mutual 
companies,  so  that  whatever  surplus  may  then  accrue  belongs 
exclusively  to  the  stockholders.  In  a  mutual  company  the  sur- 
plus is  returned  to  the  insured.  Mixed  companies  partake  of 
the  nature  of  stock  and  mutual  companies  ;  a  certain  portion  of 
the  profits  are  paid  to  the  stockholders,  and  the  remainder  is 
distributed  among  the  insured. 

Contribution — A  term  used  to  denote  the  method  of  distribu- 
ting the  surplus  of  a  company,  according  to  the  amount  each 
policyholder  has  contributed  to  produce  it. 

Discount — The  difference  between  a  sum  of  money  payable 
at  any  future  time  and  the  present  value  if  paid  immediately, 
computed  according  to  a  given  rate  of  interest. 

Dividend — The  surplus  or  profit  distributed  to  each  stock  or 
policyholder  after  the  liabilities  of  the  company  are  reserved. 
Dividends  to  policyholders  are  practically  a  misnomer.  They 
are  mainly  a  restitution  of  the  over-payments  which  have  been 
made  in  the  premises.  Reversionary  dividends,  the  allotment 
of  the  surplus  converted  into  single  premiums  to  purchase  addi- 
tional insurance  payable  according  to  the  terms  of  the  policy. 
Deferred  dividends,  those  which  are  payable  after  a  certain 
number  of  years.  Tontine  dividends,  those  which  are  payable 
on  the  tontine  method. 

Endowment — A  sum  of  money  assured  and  payable  when 
the  policyholder  arrives  at  a  certain  age.  This  is  usually  called 
"Simple  Endowment." 

For  "  Endowment  Insurance "  see  "Policy." 


OF  LIFE   INSURANCE.  13 

\ 

Expectation  of  Life — A  term  applied  to  the  mean  or  average 
duration  of  the  life  of  individuals,  after  any  specified  age  and 
according  to  a  given  table  of  mortality. 

Experience — The  data  upon  which  different  life  insurance 
tables  are  made. 

Forfeiture — The  violation  of  some  of  the  conditions  of  a 
policy  which  enables  the  company  to  cancel  the  contract  made 
with  the  policyholder. 

Ins^lrance,  Life — An  agreement  by  a  life  insurance  com- 
pany, in  consideration  of  a  stipulated  premium,  to  pay  a  certain 
sum  of  money  on  the  death  of  a  policyholder  or  upon  his  attain- 
ing a  certain  age.  Cost  of  Insurance — The  annual  tabular 
expense  which  the  company  incurs  upon  a  policy  in  force,  or  the 
amount  at  risk  multiplied  by  the  probability  of  dying  that  year. 
•Insurance  Value — The  present  value  of  the  future  cost  of  insur- 
ance assured  by  the  company  when  it  gives  a  policy  upon  the 
life  of  another.  Self  Insurance — The  amount  of  reserve  which 
is  in  the  hands  of  the  company,  or  the  amount  upon  which  the 
company  does  not  assume  any  risk  of  being  obliged  to  pay  from 
the  premiums  of  other  policyholders.  * 

Interest — A  stipulated  amount  per  annum  paid  for  the  use 
of  money. 

Lapse — The  expiration  of  the  contract  of  insurance  occa- 
sioned by  the  non-payment  of  premiums. 

Liabilities — Actual  losses  unpaid,  expenses  and  contingent 
debts  of  a  company,  for  the  payment  of  which  its  assets  are  held 
liable.  The  whole  amount  insured  is  a  contingent  debt,  but  it  is 
regarded  as  a  liability  only  to  the  extent  of  the  "  reserve  "  on 
the  policy. 

*  Assurance  and  Insurance.  "I  do  not  accept  the  distinction  laid 
down  by  some  writers  as  to  the  use  of  the  words  assurance  and  insurance, 
by  which  the  former  is  restricted  to  life  and  the  latter  to  fire  risks.  The 
more  correct  distinction  I  believe  to  be  that  a  man  insures  the  life  of  him- 
self or  of  some  other  person,  or  his  house,  or  his  ships,  or  the  fidelity  of 
his  servants,  and  that  the  office  assures  to  him  in  each  of  these  cases  a 
sum  of  money  payable  in  certain  contingencies.  Hence  the  office  is  the 
assurer  or  assurers  and  the  man  the  assured;  while  we  may  speak  of  the 
life  assured  or  the  life  insured  or  the  sum  assured  or  the  sum  insured, 
according  as  we  take  the  point  of  view  of  the  office  or  the  individual.  So 
also  we  may  speak  either  of  '  Life  Insurance'  or  '  Life  Assurance,'  as, 
for  instance,  we  may  say  that  a  man  believes  in  the  duty  and  advantage 
of  life  insurance,  in  that  a  certain  company  finds  the  business  of  life 
assurance  very  profitable."  Thomas  Bond  Sprague,  Vice-President  Insti- 
tute of  Actuaries,  London. 


!4  PRINCIPLES  AND   PRACTICE 

Loading — A  percentage  added  to  the  net  premium  in  order 
to  defray  expenses  and  provide  for  an  excess  of  mortality. 

Loss — The  payment  of  a  claim  upon  the  death  of  a  policy- 
holder.  Matured  endowments,  strictly  speaking,  are  not  losses. 

Margin — The  same  as  "  loading." 

Mortality — Having  a  given  number  of  persons  of  the  same 
age  living  at  the  beginning  of  a  year,  the  mortality  is  the  num- 
ber dying  during  that  year.  The  rate  of  mortality  is  the  ratio  of 
the  dying  to  the  number  of  living.  A  table  of  mortality  is  a 
tabulated  exhibit  of  the  number  of  survivors  and  the  number  of 
dying  each  year,  among  a  number  of  persons  taken  at  a  given 
age. 

Policy — The  contract  effected  between  the  insurer  and  the 
insured,  or  the  instrument  containing  the  terms  and  conditions. 
on  which  a  company  undertakes  to  indemnify  a  person  in  whose 
favor  a  policy  is  issued  against  the  loss  of  the  life  of  the  policy- 
holder,  or  upon  his  attaining  a  certain  age.  Life  Policy — When 
the  sum  insured  is  payable  on  the  death  of  the  policyholdeiv 
Term  Policy — One  taken  for  a  limited  number  of  years,  the  sum 
insured  payable  only  in  case  of  the  death  of  the  policy  holder  dur- 
ing this  period.  Endowment  Insurance  Policy — One  payable 
when  the  policyholder  attains  a  certain  age  or  at  death  if  it 
should  take  place  before  that  time.  Limited  Payment  Policy — 
One  in  which  the  number  of  payments  is  not  to  exceed  a  certain 
limit.  Joint  Life  Policy — One  payable  on  the  death  of  the 
first  of  two  or  more  persons  insured.  Survivorship  Policy — One 
payable  on  the  death  of  the  survivor  of  two  or  more  persons. 

Premium — The  sum  required  to  keep  a  policy  in  force  accord- 
ing to  its  conditions.  Net  Premium — The  lowest  rate,  according 
to  a  given  table  of  mortality  and  interest  at  which  an  insur- 
ance can  be  effected.  Gross,  or  Office,  Premium — The  pre- 
mium increased  by  the  loading  or  margin.  Single  Premium 
— A  sum  of  money  paid  for  insurance  and  in  consideration  of 
which  all  future  premiums  are  forborne.  The  Net  Single  Pre- 
mium is  the  present  value  of  all  future  net  annual  premiums, 
diminished  by  the  probability  of  dying  each  year. 

Premium  Notes  and  Loans — Notes  given  by  policyholders 
in  lieu  of  a  part  of  the  cash  payment  of  the  premium  ;  Loans 
are  granted  by  the  company  for  the  same  purpose.  These  notes 
or  loans  are  never  intended  to  be  paid  in  cash,  but  to  be  can- 


OF  LIFE  INSURANCE.  15 

celled  by  dividends,  or  deducted  from  the  amount  insured  in  case 
of  death. 

Present  Values — The  present  value  of  a  given  sum  payable 
at  a  certain  future  time  is  the  amount  which,  placed  at  interest, 
will  equal  this  sum  in  the  time  specified.  The  present  value  of 
an  annnity  is  the  sum  of  money  which  will  purchase,  at  a  given 
rate  of  discount,  all  the  future  payments.  The  present  value  of 
a  perpetual  annuity,  is  that  sum  which,  invested  at  a  given  rate 
of  interest,  will  always  produce  the  amount  required.  The  pre- 
sent value  of  a  deferred  annuity  is  that  sum  which,  invested  at  a 
given  rate  of  interest,  will,  at  the  end  of  the  period  during  which 
the  annuity  is  deferred,  amount  to  the  sum  which  will  then  pur- 
chase all  the  future  payments. 

Reserve — That  part  of  the  premiums  of  a  policy,  with  the 
interest  thereon,  which  is  reserved  or  set  aside  as  a  fund  for  the 
payment  of  the  policy  when  it  becomes  due. 

Reversion — A  sum  payable  on  the  occurrence  of  some  event, 
as  the  death  of  a  policyholder.  It  is  usually  applied  to  annuities 
and  surplus  on  policies,  when  payable  in  this  manner. 

Risk,  Amount  at — The  difference  between  the  sum  insured 
and  the  reserve,  or  the  amount  of  hazard  which  the  company 
assumes. 

Scrip — A  certificate  entitling  the  policyholder  to  certain 
profits  or  surplus,  when  payable. 

Solvency,  Test  of- — A  rule  to  determine  the  ability  of  a  com- 
pany to  pay  all  the  losses,  which,  according  to  a  given  table  of 
mortality  and  rate  of  interest,  may  occur. 

Surplus — The  sum  left,  after  providing  for  the  liabilities, 
claims  and  expenses  of  a  company. 

Tontine — A  fund  purchased  jointly  by  a  number  of  persons, 
the  profits  divided  among  the  oldest  survivors.  Tontine  Divi- 
dend— A  distribution  of  surplus  among  the  diminished  number 
who  are  entitled  to  it  after  a  certain  period. 

Valuation — A  method  of  finding  the  necessary  reserve  on  a 
policy. 

Value  of  a  Policy —  The  Reserve.  The  net  value  of  a  policy  is 
the  difference  between  the  net  single  premium  for  the  sum  insured 
at  the  age  of  the  policyholder  when  the  policy  is  valued,  and 
the  present  value  of  all  future  net  premiums  calculated  to  be 


i6  PRINCIPLES  AND  PRACTICE 

received  on  the  life  of  the  party  insured.  The  gross  value  of  a 
policy  is  the  difference  between  the  net  single  premium,  as  given 
above,  and  the  present  value  of  all  future  gross  premiums  to  be 
received  on  the  policy. 


INTEREST   AND   DISCOUNT. 

In  many  life  insurance  calculations,  a  great  amount  of  time 
and  labor  is  often  saved  by  a  familiarity  with  the  use  of  interest 
and  discount  tables,  there  being  many  operations  which  can  be 
done  in  a  much  more  accurate  and  expeditious  manner  by  them 
than  by  the  seriatim  method,  and  therefore  a  clear  understand- 
ing of  them  is  of  great  importance. 

COMPOUND  INTEREST. 

1 .  In  compound  interest  the  interest  of  a  given  sum  is  added  to 
the  principal,  increasing  it  at  the  end  of  each  year  or  period 
when  it  becomes  payable,  instead  of  being  paid  as  often  as  it 
becomes  due.      Thus,  at  6  per  cent,  the  amount  of  $i  for  one 
year  is  $i. 06;  the  amount  at  compound  interest  for  two  years 
is  $i.o6x$i.o6=$i.i236  ;    for  three  years  it  is  $i. 06 x $1.1236= 
$1.1910. 

2.  Tables   of  compound   interest   are  made   by  multiplying 
$i  by  the  amount  of  $i  for  one  year  at  the  given  rate  per  cent, 
and  this  product  by  the  amount  of  $i  for  one  year  which  gives 
the  amount  of  $i   for  two  years,  and  so  on  for  the  number  of 
years  required.      The   last  product  gives   the   amount   for  the 
given  number  of  years.     The   compound   interest  is  found  by 
subtracting  $i  from  it.     Thus  the  compound  interest  of  $i  for 
3  years,  at  6  per  cent,  is  $1.1910 — $1^.1910. 

3.  To  find  the  amount  of  any  sum  at  compound  interest  for  any 
number  of  years  at  a  given  rate  per  cent,  by  the  use  of  the  tables, 
we   have    only  to   look    in   the   tables,   under   the  given  rate 
per  cent,  and  opposite  to  the  required  number  of  years  for  the 
amount    of  $i    and  multiply  this  amount    by    the  given    sum. 


OF  LIFE  INSURANCE.  17 

Thus,  the  amount  of  $i  for  20  years,  at  4  per  cent,  is  $2.1911, 
and  at  7  per  cent  for  the  same  period  is  $3.8697.  The  amount 
of  $200  at  4  per  cent  would  be  $200  x  $2. 1911  =$438.22, 
and  at  7  per  cent,  $2OOx$3-S697=$773.94.  The  compound 
interest,  is  found  by  substracting  the  principal  from  the  amount 
of  the  principal  and  interest ;  thus,  $438.22 — $2oo=$238.22= 
the  compound  interest  in  the  first  case  given  above. 

4.  The  above  rule  gives  the  compound  interest  for  a  whole 
number  of  years.     To  find  the  compound  interest  for  a  number 
of  years  and  a  fractional  part  of  a  year,  we  first  find  the  amount 
by  the  tables  for  the  entire  years,  and  then  the  interest  for  the 
part  of  the  following  year,  by  subtracting  the  amount  for  the 
entire  years  required  from  the  amount  of  the  ndxt  year  in  the 
tables,  and  this  result  gives  the  interest  for  the  entire  year  of 
which  the  fractional  part  is  required.     The  next  step  is  to  find 
this  fractional  part,  and  add  it  to  the  amount  of  the  entire  year's 
principal  and  interest. 

Thus  to  find  the  amount  at  compound  interest,  4  per  cent,  or 
$i  for  20  years  and  6  months,  we  have : 

Amount  of  $i  for  20  years,     -------         $2.19112 

"        $i  for  21  years,          ---_,_  2.27876 

Compound  interest,  2ist  year,         ------  .08764 

"  "  for  6  months,        -----  .04382 

Amount  of  $i  for  20  years  and  6  months,  $2.i9ii2+$o43S2=$2.23494 
Compound  interest=$2. 23495 — $1=  -----  $1.23494 

To  find  the  compound  interest  of  $i  for  20  years  and  73 
days,  at4  per  cent,  we  have  :  $2. i9ii2  +  .oS764x-;,Tb%=$2. 191124. 
.01753 — the  amount  of  $i  for  the  given  time=$2. 20865,  and 
the  compound  interest  is  $2.20865 — $i  =$1.20865 

5.  To  find  the  time  in  which  a  given  sum  will  increase  to  a 
given  amount  at  a  given  rate  per  cent,  divide  the  given  amount 
by  the  given  sum,  and  the  result  is  the  amount  of  $i  in  the  time 
required.     By  comparing  this  result  with  the  amounts  of  $i  dur- 
ing a  series  of  years  and  at  the  given  rate  per  cent,  the  time 
required  can  easily  be  obtained. 

Example.  The  number  of  years  required  for  $200  to 
double  itself  at  compound  interest,  4  per  cent,  is  found  as 
follows:  4OO-=-2OO=2.  The  amount  of  $i  for  17  years,  at 
4  per  cent,  according  to  Table  No.  I,  is  $1.9479,  and  for  18 
years  is  $2.0258  ;  consequently  the  exact  time  required  is  be- 


18  PRINCIPLES  AND  PRACTICE. 

tween  these  two  periods,  or  $2.0258 — $i.9479=.o779,  which  is 
the  compound  interest  on  $i  during  the  eighteenth  year.  The  dif- 
ference between  1.9479  and  2  is  .0521,  and  we  have  this  propor- 
tion. If  it  requires  365  days  for  $i  during  the  eighteenth  year 
at  compound  interest  to  earn  .0779,  how  long  is  required  for  it 
to  earn  .0521  ?  By  the  rule  of  three  .0779  :  .0521  :  :  365  :  244 
days.  Hence,  the  time  required  is  17  years  and  244  days. 

6.  The  rate  per  cent  is  very  nearly  determined  by  a  similar 
method. 

Example.  If  $i  increases  to  $2  in  nine  years,  what  is  the 
rate  per  cent?  By  inspecting  Table  No.  VI,  we  find,  by  running 
the  eye  along  the  columns  opposite  to  9  years,  that  $i,  at  8  per 
cent  per  annum,  will  amount  to  $1.999,  which  shows  that  8  per 
cent  is  the  neai'est  rate  required. 

7.  To  find  the  principal  which  will  amount  to  a  certain  sum  at 
compound   interest,  the  time   and  rate  per   cent  being   given, 
divide  the  given  amount  by  the  amount  of  $r  increased  at  com- 
pound  interest,    according   to    the    required    conditions    of  the 
principal. 

Example.  To  find  the  principal,  which  will  amount  to  $2.000 
in  10  years,  at  6  per  cent  compound  interest,  we  find,  by 
Table  No.  IV,  that  the  amount  of  $i  during  this  term,  at  6  per 
cent,  is  $1.7908,  and  consequently  we  have  the  proportions 
1.7908  :  i.oo  : :  2,000  :  1,1  i6-79=the  principal  required. 

8.  It  sometimes  happens,  in  making  calculations  of  consider- 
able accuracy,  that  the  amount  of  compound  interest  of  a  certain 
sum  is  required  when  the  interest  is   added  to  the  principal 
semi-annually  or  oftener. 

When  the  interest  is  added  semi-annually,  the  following  rule 
is  a  very  expeditious  one  to  use,  provided  the  proper  tables  are 
at  hand : 

In  the  column  giving  the  amounts  of  $i  at  one-half  the 
annual  rate  of  interest  given,  take  double  the  number  of  years, 
and  proceed  as  when  the  interest  is  payable  annually. 

Example.  To  find  the  amount  at  compound  interest  of  $i 
for  10  years,  at  10  per  cent  interest,  added  semi-annually,  find 
the  amount  at  compound  interest  of  $i  for  20  years  at  5 
per  cent,  which  is  $2.6533,  the  answer  required.  To  find  the 
amount  at  compound  interest  of  $l  for  20  years  at  8  per  cent, 
interest  added  semi-annually,  find  the  amount  at  compound  in- 


OF  ZIFE  INSURANCE. 


terest  of  $i  for  40  years,  at  4  per  cent,  which  is  $4.8010,  the 
answer  required. 

9.  If  the  interest  is  added  tri-annually,  select  the  column  giving 
the   amounts   of  $i    at   one-third   the  rate  of  interest,  and  take 
three  times  the  number  of  years  ;  if  added  quarterly,  select  the 
column  giving  the  amounts  of  $i  at  one-fourth  the  rate  of  interest 
given,  and  take  four  times  the  number  of  years. 

10.  In  the  last  example  the  amount  at  compound  interest  of 
$i    for    20    years,  at   8   per    cent   interest,    added    annually,    is 
$4.660957;  semi-annually,  $4.801021  ;  quarterly,  $4.875439. 

To  find  the  amount  at  compound  interest,  added  semi-annually 
or  quarterly,  in  cases  where  the  ordinary  interest  tables  do  not 
apply,  multiply  the  principal  by  the  proper  amounts  of  $i  as 
given  in  the  following  table,  for  the  required  number  of  years  : 

THE  AMOUNTS  OF  $i  IN  ONE  YEAR,  WITH  -NTEREST  ADDED  ANNUALLY, 
HALF  YEARLY  AND  QUARTERLY. 


Rale  of 
Interest. 

How  Payable. 

Am  't  of  $'i 
in  one  year. 

Rale  of 
Interest. 

How  Payable. 

Ain't  cf$i 
in  one  year. 

4  per 
cent. 

Annually. 
Half  Yearly. 
Quarterly. 

1.040000 
1.040400 
1.040604 

7  Per- 
cent. 

Annually. 
HalfYearly. 
Quarterly. 

1.070000 
1.071225 

1.071859 

4iper 
cent. 

Annually. 
Half  Yearly. 
Quarterly. 

1.045000 
1.045506 
I-045765 

8  per 
cent. 

Annually. 
HalfYearly. 
Quarterly. 

i.oSoooo 
I.  081600  . 

1.082432 

5  Pet- 
cent. 

Annually. 
Half  Yearly. 
Quarterly. 

1.050000 
1.050625 
1.050946 

9  per 
cent. 

Annually. 
HalfYearly. 
Quarterly. 

1.090000 
1.092025 

1.093083 

6  per 
cent. 

Annually. 
HalfYearly. 
Quarterly. 

1.060000 
1.060900 
1.061364 

10  per 
cent. 

Annually. 
HalfYearly. 
Quarterly. 

I.IOOOOO 

1.102500 

1.103813 

ANNUITIES    CERTAIN   AT   COMPOUND    INTEREST. 

i.  In  the  Tables  we  have  the  amount  of  $i  per  annum,  paid  in 
advance,  and  improved  at  different  rates  of  interest,  for  any 
number  of  years  not  exceeding  50.  At  the  end  of  the  first  year 
the  amount  of  $i  at  4  per  cent  interest  is  $1.04.  At  the  be- 
ginning of  the  second  year  $i  is  added  to  this  amount,  making 
$2.04  ;  and  the  interest  on  this  sum  at  the  end  of  the  second  year 
increases  it  to  $2.1216.  This  increased  by  $i  at  the  beginning 


20  PRINCIPLES  AND  PRACTICE 

of  the  third  year  is  $3.1216,  and  at  the  end  of  the  year  it  amounts 
to  $3.2465.  By  continuing  this  process  the  columns  of  annuities 
certain  are  formed. 

2.  These  columns  may  also  be  formed  from  the  compound  in- 
terest columns,  as  illustrated  by  the  following  examples  : 

The  amount  of  $i  for  4  years  at  4  per  cent  compound  in- 
terest is  $1.1698585.  Subtracting  the  amount  of  $i  for  t  year,  we 
have  $1.1698585— 1.04=. 1298585,  and,  dividing  by  .04,  the  rate 
of  interest,  we  have  .1 298585 -=-.04= $3. 24646,  the  amount  of  $i 
per  annum  for  3  years.  The  explanation  of  this  operation  is  in 
the  fact  that  .1298585  is  the  annuity  of  .04  for  3  years,  improved 
at  4  per  cent  interest.  And  hence  we  have  the  proportion, 
..04  :  i.oo  : :  .1298585  :  3.24646. 

3.  To  find  the  amount  of  $i  per  annum  for  49  years,  take  the 
amount  of  $i   at  4  per  cent  compound  interest  for  5°  years, 
which  is  $7.1066833,  then  (7.1066833— i. 04)^.04=  15 1.66708. 

Hence,  to  find  the  annuity  certain  of  $i  per  annum  for  any 
number  of  years,  we  have  the  following  rule  :  From  the  amount 
of  $i  in  the  compound  interest  columns  at  the  given  rate  per  cent, 
and  taken  at  the  given  number  of  years  plus  one,  subtract  the 
amount  of  $i  for  one  year  at  the  given  rate,  and  divide  the  re- 
mainder by  the  rate  per  cent. 

4.  When  the  annuity  is  payable  at  the  end  of  the  year,  as  in  the 
old  English  tables,  instead  of  at  the  beginning,  the  rule  is  as 
follows : 

From  the  amount  at  compound  interest  in  the  tables,  at  the 
given  rate  per  cent,  and  taken  at  the  given  number  of  years,  sub- 
tract $i,  and  divide  the  remainder  by  the  rate  per  cent,  and 
the  quotient  is  the  amount  of  an  annuity  of  $i  for  that  term. 

Thus,  in  the  last  example,  the  amount  of  $i  for  50  years  is 
7.1068833  ;  subtracting  $i,  we  have  6.io6S833-^-.o4=$i52.667o8, 
the  amount  of  $i  per  annum  for  50  years,  instead  of  49  years,  as 
in  the  previous  rule. 

In  this  example,  deducting  $i  from  the  amount,  we  have  the 
annuity  certain  of  .04  for  50  years  at  compound  interest;  there- 
fore, .04:  $i  : :  $6.1066833  :  $152.66708. 

5.  In  life  insurance  it  is  often  necessary  to  make  such  calcula- 
tions as  the  following,  in  order  to  estimate  the  probable  advan- 
tages of  accepting  a  risk : 

If  an  annual  net  premium  on  a  life  policy  of  $1,000  is  $23.68, 


OF  LIFE  INSURANCE.  21 

how  long  will  it  be  necessary  for  the  insured  to  l\ve,  in  order  that 
the  company  may  realize  the  amount  insured? 

Dividing  $1,000  by  $23.68,  we  have  $43.2297;  therefore,  it 
would  require  the  same  time  which  it  takes  $i  per  annum  at 
7  per  cent  compound  interest  to  amount  to  this  sum.  By  Table  V, 
we  find  that  $i  per  annum,  for  19  years,  at  7  per  cent,  amounts 
to  $39-9955)  and  for  20  years  the  amount  is  $43.8652.  It  is  evi- 
dent, then,  that  the  time  required  is  between  19  and  20  years. 
The  exact  date  is  thus  found.  At  the  beginning  of  the  twentieth 
year,  as  the  premiums  are  payable  in  advance,  the  amount  of 
$i  per  annum  would  be  $39-9955+$  i =$40.9955.  The  difference 
between  this  and  $42.2297  is  $1.2342,  which  is  the  amount  of  in- 
terest required  to  be  earned  after  the  beginning  of  the  twentieth 
year.  The  total  amount  of  interest  earned  during  the  twentieth 
year  is  $43.8652— $4O.9955=$2.8697-  Therefore,  we  have  the 
proportion,  if  it  requires  i  year  for  $40.9955  to  earn  $2.8697  m" 
terest,  how  long  does  it  require  to  earn  $1.2342,  or  $2.8697: 
$1.2342  : :  365  1157  days.  That  is,  it  would  require  19  years  and 
157  days,  or  twenty  premiums  and  the  interest  thereon  for  157 
days  after  the  twentieth  premium  is  paid. 

PRESENT  VALUES  AND  DISCOUNT. 

A  familiarity  with  the  present  values  of  sums  payable,  is  quite 
as  important  as  that  of  interest. 

1.  The  present  value  of  $i  for  one  year  at  6  per  cent  discount, 
is  the  sum  which,  placed  at  6  per  cent  interest  for  i  year,  will 
amount  to  $i.     This  quantity  is  found  by  the  following  propor- 
tion :  if  $i  will  amount  to  $1.06  in  i  year,  what  sum  is  required 

to  amount  to  $i  ?  or  $1.06  :  $i  : :  $i  :  .943396,  or  |- -^ =.943396. 

vp  I  .OO 
~n  i  c    ef        c  •  $I.OO  $I.OO 

The    present  value  of  $i    for  2  years  is  5 —          — z=J-     ,= 

/  $i.o6x$i.o6    $1.236 

00  /•  i    r  $I.OO  $I.OO  0         /- 

.889996  ;  and  for  -*  years  * — , — ;       ,    ... — 2=^     —,=.8-59610. 
0  J  $i.o6x$i.o6x$i.o6    $1.191016        oy      y 

In  this  manner  the  columns  of  present  values  are  found. 

2.  To  find  the  number  of  years  which  the  payment  of  a  sum 
of  money  must  be  deferred  in  order  that  it  may  have  a  certain 
present  value,  divide  the  given  present  value  by  the  amount  and 
the  result  is  the  present  value  of  $i    for  the  time  required.     By 
comparing  this  result  with  the  present  values  of  $i  during  a  series 


22  PRINCIPLES  AND  PRACTICE 

of  years  and  at  the  given  rate  per  cent,  as  given  in  the  tables, 
the  time  required  can  be  obtained. 

Let  it  be  required  to  find  the  number  of  years  which  the  pay- 
ment of  $i  must  be  deferred  to  have  a  present  value  of  .50 
at  6  per  cent  discount.  By  referring  to  Table  IV,  we  find  in  the 
6  per  cent  column  that  the  present  value  of  $i  for  n  years  is 
.526788,  and  at  12  years  it  is  .496969;  the  difference  between 
these  two  quantities  is  .029819.  The  difference  between  .526788 
and  .50  is  .026788.  To  find  the  number  of  days  required  in  ad- 
dition to  the  1  1  years,  we  have  the  following  proportion  :  if  it 
requires  one  year  for  the  present  value  of  $i  at  the  end  of  n 
years  to  diminish  .029819,  how  long  will  it  require  to  diminish 
.026788  ?  and  the  ratios  are  stated  as  follows  :  .029819  :  .026788  :  : 
365:328  days.  Hence  the  time  required,  n  years  and  328 
days. 

3.  To  find  the  rate  per  cent  of  discount  required  for  a  given 
sum  to  have  a  certain  present  value  in  a  given  number  of  years, 
we  find  the  present  value  of  $i  according  to  the  terms  given,  and 
compare  this  result  with  the  present  values  of  $i  in  the  tables 
at  the  required  number  of  years. 

Thus  to  find  the  rate  per  cent  required  for  $i,  payable  14 
years  hence,  to  have  a  present  value  of  .50,  we  divide  .50  by 
$i,  and  we  have  the  result  .50,  then,  by  inspecting  the  columns 
of  present  values  along  the  lines  representing  the  values  of  $i, 
payable  14  years  hence,  we  find,  under  the  5  per  cent  column, 
that  the  present  value  of  $i  is  .505068,  which  indicates  that  5  per 
cent  is  very  nearly  the  rate  required. 

4.  The  present  value  of  $i  per  annum,  at  the  end  of  each  year 
for  any  number  of  years,  is  the  present  value  of  $i  for  one  year, 
plus  the  present  value  of  $i  for  two  years,  plus  the  present  value 
of  $i  for  three  years,  and  so  on.     By  referring  to  Table  II,  we 
find  the  present  value  of  $i,  at  4^  per  cent  for  one  year,  is 
.956938,  and  for  two  years,  is  .915730.     Adding  these  together, 
we  have  1.872668=  the  present  value  of  $i  per  annum  for  two 
years.     The  present  value  of  $i,  per  annum,  for  three  years,  is 


5.  The  present  value  of  $i,  per  annum,  for  any  number  of 
years,  at  any  given  rate  per  cent,  may  be  easily  found  by  the 
following  rule:  Subtract  the  present  value  of  $i,  as  found 
in  the  tables,  for  the  given  time  and  rate,  from  unity,  or  $i, 


OF  LIFE  INSURANCE. 


23 


and  divide  this  difference  by  the  given  rate  for  $i,  the  result 
will  be  the  required  present  value  of  $i,  per  annum.  Thus,  in 
the  last  example  we  have  $i—  .876297=.  123703  -4-.O45=$2.  74896. 

The  quantity  .123703  becomes  the  present  value  of  4  1-2  cents, 
payable  annually  for  three  years,  and  hence  .123  703-5-  .045= 
2.74896,  or  .045  :  123703  :  :  i.oo  :  2.74896. 

6.  The  present  value  of  a  perpetual  annuity  is  the  sum  which, 
paid  now  and  invested  at  a  given  rate  per  cent,  will  produce  the 
annuity.  To  find  the  present  value  of  the  perpetual  annuity  of 
$i  at  5  per  cent  interest,  we  have  the  following  proportion  : 
.05  :  .1  :  :  i  :  20,  or  $i  divided  by  the  given  rate  per  cent,  will 
give  the  present  value  of  the  perpetual  annuity  of  $i,  and 
from  this  the  present  value  of  any  other  sum  may  be  found. 

7-  In  making  calculations  by  means  of  these  tables,  care  should 
be  taken  to  examine  whether  the  annuity  is  payable  at  the 
beginning  or  at  the  end  of  the  year.  In  the  above  example  the 
present  value  of  $i  payable  at  the  beginning  of  the  first  year 
is  $i  ;  for  the  second  year  $1.9569;  for  the  third  year 
$2.8727  ;  for  the  fourth  year  $3.7490,  and  so  on.  This  caution 
becomes  the  more  necessary  as  all  life  insurance  premiums  are 
regarded  as  being  paid  at  the  beginning  of  each  year,  while  an- 
nuities are  usually  payable  at  the  end. 

8.  The  present  value  of  the  premium  $23.68  for  twenty  years, 
at  seven  per  cent  discount,  the  first  premium  being  paid  in  ad- 
vance, is  computed  thus  :  ($10.335595  +  1) 


DEFERRED  ANNUITIES. 

1.  The  present  value  of  a  deferred  annuity  certain  of  $i,  pay- 
able at  the  end  of  the  year,  deferred  for  four  )rears,  and  then  to 
continue  six  years,  at  6  per  cent  discount,  is  found  by  taking  the 
difference  between  the  present  value  of  $i  for  the  whole  annuity 
term  and  the  present  value  of  $i  for  the  deferred  term  ;  thus,  by 
Table  IV,  7.360087-3.465  1  06=  $3.  894981. 

2.  To  find  the  present  value  of  an  annuity  certain  to  continue 
a  given  number  of  years,  after  a  given  term,  multiply  the  differ- 
ence of  the  present  value  of  $i  per  annum  for  the  whole  term, 
and  of  $i  per  annum  for  the  deferred  term  by  the  given  an- 
nuity ;  the  result  will  be  the  required  value. 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  I. 
MONETARY  TABLES,  4  PER  CENT. 


N 

Tears. 

Amount  of$i 
in  N  years. 

Present 
Value  of  $i 
due  N  years 
hence. 

Amount  of 
$  i  per  annum 
in  N  years. 

Present 
Value  of  $i 
per  annum  for 
N  years. 

Sinking 

fund  Unit  will 
amount  to  §i 
in  N  years. 

I 

1.0400 

.961538 

1.0400 

.9615 

•96l54 

2 

.0816 

.924556 

2.1216 

I.8S6I 

•47  '34 

3 

.1249 

.888996 

3-2465 

2-7751 

.30802 

4 

.1699 

.854804 

4-4I63 

3.6299 

.22643 

5 

.2167 

.821927 

5-6330 

'  4-45I8 

•17753 

6 

•2653 

•TQOS1.? 

6-8983 

5.2421 

.14496 

7 

•3!59 

.759918 

8.2142 

6.OO2I 

.12174 

8 

.36S6 

.730690 

9.5828 

6.7327 

•10435 

9 

•4233 

.702587 

11.0061 

7-4353 

.09086 

10 

.4802 

•675564 

12.4864 

8.1109 

.08009 

ii 

•5395 

.649581 

14.0258 

8.7605 

.07130 

12 

.6010 

.624597 

15.6268 

9-3851 

.06399 

J3 

.6651 

.600574 

17.2919 

9.9856 

•05783 

*4 

•73^7 

•577475 

190236 

10.5631 

•05257 

15 

.8009 

•555265 

20.8245 

11.1184 

.04802 

16 

.8730 

•5339°S 

22.6975 

11.6523 

.04406 

17 

•9479 

•513373 

24.6454 

12.1657 

.04058 

18 

2.02  S8 

.493628 

26.6712 

12.6593 

•03/50 

J9 

2.1068 

.474642 

28.7781 

I3-I339 

•03475 

20 

2.1911 

•456387  . 

30.9692 

i3-5903 

.03229 

21 

2.2788 

•438834 

33-248o 

14.0292 

.03008 

22 

2.3699 

•421955 

35-6i79 

H-45U 

.02808 

23 

2.4647 

•405726 

38.0826 

14.8568 

.02626 

24 

2.5633 

.390121 

40.6459 

15.2470 

.02460 

25 

2.6658 

•375"7 

43-3II7 

15.6221 

.02309 

26 

2.7725 

.360689 

46.0842 

15.9828 

.02  i  70 

27 

2.8*34 

.346817 

48.9676 

16.3296 

.02042 

23 

2.9987 

•333477 

51.9663 

16.6631 

.01924 

29 

3.1187 

.320651 

55-oS49 

16.9837 

.01816 

3° 

3-2434 

.308319 

58-3283 

17.2920 

.01714 

31 

3-3731 

.296460 

61.7015 

17-5885 

.01621 

33 

3-  5"Si 

.285058 

65.2095 

17.8736 

•01534 

33 

3.6484 

.274094 

68.0579 

18.1476 

.01452 

34, 

3-7943 

•263552 

72-6522 

18.4112 

.01376 

35 

3-946i 

•253415 

76.5983 

18.6646 

.01306 

36 

4.1039 

.243669 

80.7022 

18.9083 

.01239 

37 

4.2681 

•234297 

84.9703 

19.1426 

.01177 

33 

4.4388 

.225285 

89.4091 

19.3679 

.01119 

39 

4.6164 

.216621 

94-0255 

I9-5845 

.01064 

40 

4.8010 

.208289 

98.8265 

19.7928 

.OIOI2 

4i 

49931 

.200278 

103.8196 

19.9931 

.00963 

42 

5.1928 

•i92575 

109.0124 

20.1856 

.00917 

43 

5-4005 

.185168 

114.4129 

20.3708 

.00874 

44 

5-6165 

.178046 

120.0294 

20.5488 

.00833 

45 

5.8412 

.171198 

125.8706 

20.7200 

.00794 

46 

6.0748 

.164614 

131-9454 

20.8847 

.00758 

47 

6.3178 

.158283 

138.2632 

21.0429 

.00723 

48 

6,5705 

•152195 

I44-8337 

21.1951 

.00691 

49 

6-8333 

.146341 

151.6671 

21-3415 

.00659 

50 

7.1067 

.140713 

158.7738 

21.4822 

.00630 

OF  LIFE  INSURANCE 


TABLE  No.  II. 
MONETARY  TABLES,  4^  PER  CENT. 


N 

Tears. 

Amount  of  $i 
»'/;  N  years. 

Present 
Value  of  $i 
due  N  years 
hence. 

Amount  of 
$  i  per  annum 
in  N  years. 

Present 
Value  of  $i 
per  annum  for 
N  years. 

Sinking 
fund  Hint  tvill 
amount  to  $i 
in  N  years. 

I 

1.0450 

•956938 

1.0450 

0.9569 

•95695 

2 

1.0920 

•9!5730 

2.1370 

1.8727 

•46795 

3 

I.I4I2 

.876297 

3.2782 

2.7490 

•30505 

4 

1.1925 

.838561 

4.4707 

3-5875 

.22368 

5 

1.2462 

.802451 

5-7I69 

4.3900 

.17494 

6 

1.3023 

.767896 

7.0192 

5-^579 

•14247 

7 

1.3609 

.734828 

8.3800 

5-8927 

•"933 

8 

1.4221 

•703185 

9.8021 

6-5959 

.10202 

9 

1.4861 

.672904 

II.2SS2 

7.2688 

.088^9 

10 

1-5530 

.643928 

12.8412 

7.9127 

.07788 

ii 

1.6229 

.616199 

14.4640 

8.5289 

.06914 

12 

1.6959' 

.  .589664 

16.1599 

9.1186 

.06188 

13 

1.7722 

.564272 

17.9321 

9.6829 

•05577 

H 

1.8519 

•539973 

19.7841 

10.2228 

•05055 

15 

1-9353 

'  .516720 

21.7193 

10-7395 

.04604 

16 

2.0224 

•494469 

23-74I7 

11.2340 

.04212 

17 

2.1134 

•473  !  /6 

25-855I 

11.7072 

.03868 

18 

2.2085 

.452800 

28.0636 

12.1600 

•03563 

J9 

2.3079 

•433302 

30-37H 

12.5933 

•03^93 

20 

2-4117 

.414643 

32-7S3I 

13.0079 

.030^0 

21 

2.5202 

.396787 

35-3034 

13-4047 

•02833 

22 

2-6337 

.379701 

37.9370 

13-7844 

.02636 

23 

2.7522 

•363350 

40.6892 

14.1478 

,02458 

24 

2-8760 

•347703 

43-5652 

14-4955 

•02295 

25 

3-0054 

•332731 

46.5706 

14.8282 

•02147 

26 

3-M07 

.318402 

49-7  "3 

15.1466 

.02012 

=7 

3.2820 

.304691 

52-9933 

15-4513 

.01887 

28 

3-4297 

.291571 

56.4230 

15-7429 

.01772 

29 

3-5840 

.279015 

60.0071 

16.0219 

.01667 

3° 

3-7453 

.267000 

63-7524 

16.2889 

.01569 

31 

39'39 

•255502 

67.6662 

16.5444 

.01478 

32 

4-0900 

•24450° 

71.7562 

16.7889 

.01394 

33 

4-2740 

•233971 

76.0303 

17.0229 

.01316 

34 

4.4664 

.223896 

80.4966 

17.2468 

.01242 

35 

4.6673 

•214254 

85.1640 

17.4610 

.01174 

36 

4.8774 

.205028 

900413 

17.6660 

.OI  MI 

37 

5.0969 

.196199 

95.1382 

17  8622 

.01051 

38 

5-3-6-2 

.187750 

100.4644 

18.0500 

.00996 

39 

5-56?9 

.179665 

106.0303 

18.2297 

.00043 

40 

5.8164 

.171929 

111.8467 

18.4016 

.00894 

4i 

6.0781 

.164525 

117.9248 

185661 

.00848 

42 

6-35  J6 

•157440 

124.2764 

18.7235 

.00804 

43 

6-6374 

.150661 

130.9138 

18.8742 

.00764 

44 

6.9361 

•H4I73 

137.8500 

19.0184 

.00725 

45 

7.2482 

.137964 

145.0982 

19-  '563 

.00689 

46 

7-5744 

.132023 

152.6726 

19.2884 

.00055 

47 

7-9  '53 

.126338 

1  60.  =1879 

19.4147 

.00f>23 

48 

8.2715 

.120898 

168.8594 

I9-5356 

.00592 

49 

8-6437 

.115692 

177-5030 

19.6513 

.00563 

50 

9.0326 

.110710 

186.5357 

19.7620 

.00536 

26 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  III. 
MONETARY  TABLES,   5  PER  CENT. 


N 

Amount  q/"$i 

Present 
Value  of  $i 

Amount  of 

Present 

Value  of  $i 

Sinking 
fund  that  ivill 

hence. 

in  N  years. 

Jor  N  years. 

N  years. 

I 

1.0500 

.952381 

1.0500 

•9524 

•95238 

2 

I.IO25 

.907029 

2-I525 

1.8594 

.46458 

3 

1.1576 

.863838 

3-3JOI 

2.7232 

.30211 

4 

.822702 

4.15256 

3-5460 

.22097 

5 

1.2763 

•783526 

5.8019 

.17236 

6 

I.340I 

.746215 

7.1420 

5-0757 

.14002 

7 

1.4071 

.710681 

8.5491 

5.7864 

.11697 

8 

1-4775 

.676839 

10.0266 

6.4632 

•°9973 

9 

I-55I.3 

.644609 

"•5779 

7.1078 

.08637 

10 

1.6289 

.613913 

13.2068 

7.7217 

•07572 

ii 

1.7103 

.584679 

14.9171 

8.3064 

.06704 

12 

1-7959 

.556837 

16.7130 

•  8.8633 

•05983 

13 

1.8856 

.530321 

18.5986 

9-3936 

•°5377 

'4 

1.9799 

.505068 

20.  15786 

.  9.8986 

.04859 

15 

2.0789 

.481017 

22.6575 

IO-3797 

.04414 

16 

2.1829 

.458112 

24.8404 

10.8378 

.04026 

17 

2.2920 

•436297 

27.1324 

11.2741 

.03686 

18 

2.4066 

•4I552I 

29-5390 

11.6896 

•03385 

19 

2.5270 

•395734 

32.0660 

12.0853 

.03119 

20 

2-6533 

.376889 

34-7193 

12.4622 

.02880 

21 

2.7860 

•358942 

37-5052 

12.8212 

.02666 

22 

2-9253 

.341850 

40.4305 

13.1630 

•02473 

23 

3-0715 

•325571 

43.5020 

13.4886 

.02299 

24 

3-2251 

.310068 

46.7271 

13.7986 

.02140 

25 

3.3864 

•295303 

5°-  "35 

14.0939 

.01996 

26 

3-5557 

.281241 

53.6691 

'4-3752 

.01863 

27 

3-7335  ' 

.267848 

57.4026 

14.6430 

.01742 

28 

3.9201 

•255094 

61.3227 

14.8981 

.01631 

29 

4.1161 

.242946 

65.4388 

15.1411 

.01528 

30 

4.3219 

•231377 

69.7608 

I5-3725 

.01434 

31 

4-538o 

.220359 

74.2988 

.01346 

32 

4.7649 

.209866 

79.0638 

15.8027 

.01265 

33 

5-0032 

.199873 

84.0670 

16.0025 

.01190 

34 

5-2533 

.190355 

893203 

16.1929 

.OII20 

35 

.181290 

94-8363 

16.3742 

•01055 

36' 

5-7918 

.172657 

100.6281 

16.5469 

.00994 

37 

6.0814 

.164436 

106.7095 

16.7113 

.00937 

38 

6-3855 

.156605 

113.0950 

16.8679 

.00884 

39 

6.7048 

.149148 

119.7998 

17.0170 

.00835 

40 

7.0400 

.142046 

126.8398 

17.1591 

.00788 

41 

7.3920 

.135282 

134.2318 

17.2944 

.00745 

42 

7.7616 

.128840 

I4I-9933 

17.4232 

.00704 

43 

8.1497 

.122704 

150.1430 

17-5459 

.OO666 

44 

8-5572 

.116861 

1158.7002 

17.6628 

.00630 

45 

8.9850 

.111297 

167.6852 

17.7741 

.00597 

46 

9-4343 

.105997 

177.1194 

17.8801 

.00565 

47 

9.9060 

.100949 

187.0254 

17.9801 

•00535 

48 

10.4013 

.096142 

197.4267 

18  0772 

.00506 

49 

10.9213 

.091564 

208.3480 

18.1687 

.00480 

50 

11.4674 

.087204 

219.8154 

18.2559 

•00455 

OF  LIFE  INSURANCE, 


TABLE   No.    IV. 
MONETARY  TABLES,  6  PER  CENT. 


N 
Tears. 

! 
Amount  of  '$i 
i»  N  years. 

Present 

•value  of  $i 
due   N  years 
hence. 

Amount  of 
$i  per  annum 
in  N  years. 

Present 
Value  o/"$i, 
per  annum  for 
N  years. 

Sinking 
\  fund  ihnt  will 
amount  to  $i  in 
N  years. 

I 

1.  0600 

•943396 

I.  0600 

0-9434 

.Q4340 

2 

1.1236 

.889996 

2.1836 

1-8334 

•45796 

3 

1.1910 

.839619 

3-3746 

2.6730 

•29633 

4 

1.2625 

.792094 

4-6371 

3-465I 

•21565 

5 

I-3382 

•747258 

5-9753 

4.2124 

•16735 

6 

1.4185 

.704961 

7-3938 

4-9173 

•13525 

7 

I-5036 

.665057 

8.8975 

5-5824 

.11239 

8 

I-593S 

.627412 

10.4913 

6.2098 

•09532 

9 

1.6895 

.591898 

12.1808 

6.8017 

.0821O 

10 

1.7908 

•558395 

13.9716 

7.3601 

•07157 

ii 

1.8983 

.526788 

15.8699 

7.8869 

.06301 

12 

2.0122 

.496969 

17.8821 

8.3838 

•05592 

13 

2.1329 

•468839 

20.0151 

8.8527 

.04996 

14 

2.2609 

.442301 

22.2760 

9.2950 

.04489 

15 

2.3966 

•417265 

24.6725 

9.7122 

•04053 

16 

2.5404 

•393646 

27.2129 

10.  1059 

•03675 

17 

2.6928 

•371364 

29.9057 

10-4773 

•03344 

18 

2-S543 

•350344 

32.7600 

10.8276 

•03053 

19 

3-0256 

•330513 

35-7856 

11.15^1 

.02794 

20 

3.2071 

.311805 

38.9927 

11.4699 

•02565 

21 

3-3996 

•294155 

42-3923 

11.7641 

•02359 

22 

3-6035 

•277505 

45-9958 

12.0416 

.02174 

23 

3-8i97 

.261797 

49.8156 

12.3034 

.O?OO7 

24 

4.0489 

•246979 

53-8645 

12.5504 

.01857 

25 

4.2919 

.232999 

58.1564 

12.7834 

.01720 

26 

4-5494 

.ZigSlO 

62.70^8 

13.0032 

•01595 

27 

4.8223 

.207368 

67-5281 

13.2105 

.01481 

28 

5-ni7 

.195630 

72.6398 

13.4062 

•01377 

29 

5-4184 

•184557 

78.0582 

I3-5907 

.01281 

30 

5-7435 

.I74IIO 

83.8017 

13.7648 

.01193 

31 

6.0881 

.164255 

89.8898 

139291 

.OIII2 

32 

6-4534 

•154957 

96-3432 

14.0840 

.01038 

33 

6.8406 

.146186 

103.1838 

14.2302 

.00969 

34 

7.2510 

.137912 

110.4348 

14.3681 

.00905 

35 

7.6861 

.130105 

118.1209 

14.4982 

.00847 

36 

8-H73 

.122741 

126.2681 

14.6210 

.00792 

37 

8.6361 

•"5793 

134.9042 

14.7368 

.00741 

38 

9-J543 

•109239 

144.0^85 

14.8460 

.00694 

39 

9-7035 

.103056 

153.7620 

14.9491 

.00651 

40 

10.2857 

.097222 

164.0477 

15.0463 

.00610 

4i 

10.9029 

.091719 

1  74-  9505 

15.1380 

.00572 

42 

"•5570 

.086527 

186.5076 

15-2245 

.00536 

43 

12.2505 

.081630 

198.7580 

15.3062 

.C0503 

44 

12.9855 

.077009 

2H-7435 

15-3832 

.C0472 

45 

13.7646 

.072650 

225.5081 

15-4558 

.00443 

46 

I4-5905 

.068^38 

240.0986 

I5-5244 

.00417 

47 

15-4659 

.064658 

255-5645 

15.5890 

.00392 

48 

16.3939 

.060998 

271.9584 

15.6500 

.00368 

49 

17-3775 

•057546 

289.3359 

15.7076 

.00346 

50            18.4202 

.054288 

3°7-7.s6i 

15.7619 

•00325 

28 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  V. 
MONETARY  TABLES,  7  PER  CENT. 


N 

Years. 

Amount  of  $i 
tit  N  years. 

Present 
Value   of  $i 
due  N  years 
hence. 

Amount  of 
$i  per  annum 
in  N  years. 

Present 

Value  of  $i 
per  annum  for 
N  years. 

Shikiiiff 
fund  that  iv  ill 
amount  to  $1 
in  N  years. 

I 

1.0700 

•934579 

I.O7OO 

•9346 

•93458 

2 

1.1449 

•873439 

2.2149 

I.  8080 

•45H9 

3 

1.2250 

.816298 

3-4399 

2-6243 

.29071 

4 

1.3108 

.762895 

4-7507 

3-3S72 

.21050 

5 

1.4026 

.712986 

6.1533 

4.1002 

.16251 

6 

1.5007 

.666342 

7.6540 

4.7665 

.13065 

7 

1.6058 

.622750 

9.2598 

5-3S93 

.10799 

8 

1.7182 

.582009 

10.9780 

5.9713 

.09109 

9 

1-8385 

•543934 

12.8164 

6-5152 

.07803 

10 

1.9672 

•508349 

14.7836 

7.0236 

.06764 

ii 

2.1049 

•475093 

I6.S8S5 

7.4987 

.05921 

12 

2.2522 

.444012 

19.1406 

7-9427 

.05224 

13 

2.4098 

.414964 

21-5505 

8-3577 

.04640 

H 

2-5785 

.387817 

24.1290 

8-7455 

.04144 

15 

2.7590 

.362446 

26.8881 

9.1079 

•03719 

16 

2-9S22 

•338735 

29.8402 

9.4466 

•03351 

17 

3-I5S8 

•316574 

32.9990 

9.7632 

.03030 

18 

3-3799 

•29.5864 

36.3790 

10.0591 

.02749 

19 

3-6165 

.276508 

39-9955 

10.3356 

.02500 

20 

3.8697 

.258419 

43.8652 

10.5940 

.02280 

21 

4.1406 

.241513 

48.0057 

10.8355 

.02083 

22 

4.4304 

.225713 

52.4361 

n.  0612 

.01907 

23 

4-7405 

.210947 

57.1767 

11.2722 

.01749 

24 

5.0724 

.197147 

62.2490 

11.4693 

.Ol6o6 

25 

5-4274 

.184249 

67.6765 

11.6536 

.01478 

26 

.5.8074 

.172195 

73-4838 

11.8258 

.01361 

27 

6.2139 

.160930 

79.6977 

11.9867 

•01255 

28 

6.6488 

.150402 

86.3465 

12.1371 

.01158 

29 

7-IH3 

•140563 

93.4608 

12.2777 

.OIO7O 

30 

7.6123 

•131367 

101.0730 

12.4090 

.00989 

31 

8.1451 

.122773 

109.2182 

12.5318 

.00915 

32 

8.7153 

.114741 

"7-9334 

12.6466 

.00848 

33 

9-3253 

•J07235 

127.2588 

12.7538 

.00786 

34 

9.9781 

.100219 

137-2369 

12.8540 

.00729 

35 

10.6766 

.093663 

H7-9I35 

12.9477 

.00676 

36 

11.4239 

•087535 

159-3374 

13.0352 

.00628 

37 

12.2236 

.081809 

171.5610 

13.1170 

.00583 

33 

i3-0793 

.076457 

184.6403 

i3-!935 

.00542 

39 

13.9948 

.07H55 

198.6351 

13.2649 

.00503 

40 

14-9745 

.066780 

213.6006 

I3-33I7 

.00468 

4i 

16.0227 

.062412 

229.6322 

i3.394r 

•00435 

42 

I7-M43 

.058329 

246.7765 

I3-4524 

.00405 

43 

18.3444 

•054513 

265.1209 

I3-5070 

•00377 

44 

19.6285 

.050946 

284.7493 

I3.5579 

.00351 

45 

21.0025 

.047613 

305-75i8 

13-6055 

.00327 

46 

22.4726 

•044499 

328.2244 

13.6500 

.00305 

47 

24.0457 

.041587 

352.2701 

13.6916 

.00284 

48 

25.7289 

.038867 

377,9990 

13-7305 

.00265 

49 

27.5299 

.036324 

405.5289 

13.7668 

.00247 

50 

29.4570 

•033948 

434.9860 

13.8007 

.00230 

OF  LIFE  INSURANCE. 


TABLE  No.  VI. 
MONETARY  TABLES,  8  PER  CENT. 


N 

Tears. 

Amount  of$t 
in  ti  years. 

Present 
Value  of  $i 
due  N  years 
hence. 

Amount  of 
$\fer  annum 
in  N  years. 

Present 

Value  of  $i 
per  annum  for 
N  years. 

Sinking' 

fund  that  mill 
amount  to  $i 
in  nysars. 

I 

I.  0800 

.925926 

1.  0800 

•9259 

•92593 

2 

1.1664 

•857339 

2.2464 

L7833 

.44516 

3 

1-2597 

•793832 

3.5061 

2-5771 

.28522 

4 

I-3605 

•735030 

4.8666 

3-3I2I 

.20548 

5 

1.4693 

.680583 

6-3359 

3-9927 

•15783 

6 

1.5869 

.630170 

7.9228 

4.6229 

.12622 

7 

I.7I38 

•583490 

9.6366 

5.2064 

•10377 

8 

1.8509 

.540269 

11.4876 

5.7466 

.08705 

9 

1.9990 

.500249 

13.4866 

6.2469 

.  -074H 

10 

2.1589 

•463193 

I5-6455 

6.7101 

.06392 

ii 

2.3316 

.428883 

17.9771 

7-I390 

•05563 

12 

2.5182 

•397"4 

20.4953 

7-536I 

.04879 

13 

2.7196 

.367698 

23.2149 

7-9038 

.04308 

14 

2.9372 

.340461 

26.1521 

8.2442 

.03824 

IS 

3.1722 

.315242 

29-3243 

8-5595 

.03410 

16- 

3-4259 

.291890 

32.7502 

8.8514 

•03053 

17 

3.7000 

.270269 

36.4502 

9.1216 

.02744 

18 

3.9960 

.250249 

40.4463 

93719 

.02472 

*9 

4-3I57 

.231712 

44.7620 

9.6036 

.02234 

20 

4.6610 

.214548 

49.4229 

0.8181 

.02023 

21 

5-0338 

.198656 

54-4568 

10.0168 

.01836 

22 

5-4365 

.183941 

59-S933 

10.2007 

.01670 

23 

5-8715 

•I703I5 

65.7648 

10.3711 

.01521 

24 

6.3412 

.157699 

72.1059 

10.5288 

.01387 

25 

6.8485 

.146018 

78-9544 

10.6748 

.01267 

26 

7-3964 

.135202 

86.3508 

10.8100 

.01158 

27 

7.9881 

.125187 

94-3388 

10.9352 

.01060 

28 

8.6271 

.115914 

102.9659 

11.0511 

.00971 

29 

9-3I73 

.107328 

112.2832 

11.1584 

.00891 

30 

10.0627 

•099377 

122.3459 

11.2578 

.00817 

31 

10.8677 

.092016 

I33-2I35 

11.3498 

.00751 

32 

"-737I 

.085200 

144.9506 

"•4350 

.00690 

33 

12.6760 

.078889 

157.6267 

".5139 

.00634 

34 

13.6901 

•073045 

171.3168 

11.5869 

.00584 

35 

I4-7853 

.067635 

186.1021 

11.6546 

•00537 

36 

15.9682 

.062625 

202.0703 

11.7172 

.00495 

37 

17.2456 

.057986 

2I9-3I59 

11.7752 

.00456 

33 

18.6253 

.053690 

237.9412 

11.8289 

.00421 

39 

20.1153 

.049713 

258.0565 

11.8786 

.00387 

40 

21.7245 

.046031 

279.7810 

11.9246 

•00357 

4i 

23.4625 

.042621 

303-2435 

11.9672 

.00330 

42 

25-3395 

•039464 

328.5830 

12.0067 

.00304 

43 

27.3666 

.036541 

355  '9496 

12.0432 

.00281 

44 

29.5560 

•033834 

385.5056 

12.0771 

.00259 

45 

31.9204 

.031328 

417.4261 

12.1084 

.00240 

46 

34-4741 

.029007 

451.9002 

12.1374 

.00221 

47 

37.2320 

.026859 

489.1322 

12.1643 

.O0204 

48 

40.2106 

.024869 

529-3427 

12.1891 

.OOlSg 

49 

43-4274 

.023027 

572.7702 

12.2122 

-00175 

50 

46.9016 

.021321 

619.6718 

".2335 

.00161 

PRINCIPLES  AND  PRACTICE 


TABLE  No.  VII. 
MONETARY  TABLES,  9  PER  CENT. 


N 

Years. 

Amount  of  $i 
»'«  N  years. 

Present 
Value  of  $1 
due  N  years 
hence. 

Amount  of 
$i  per  annum 
in  N  years. 

Present 
Value  of  $  i 
per  annum  for 
N  years. 

Sinking 
fund  that  -will 
amount  to$i 
in  N  years. 

I 

I.OgOO 

•9I743I 

I.  ogOO 

0.9174 

•9!743 

2 

1.1881 

.841680 

2.2781 

I-759I 

.43896 

3 

1.2950 

.772184 

3-5731 

2.53I3 

.27987 

4 

1.4116 

.708425 

4.9847 

3-2397 

.20061 

5 

1-5386 

.649931 

6.5233 

3.8897 

•15330 

6 

1.6771 

.596267 

8.2004 

4.4859 

.12195 

7 

1.8280 

•547034 

10.0285 

5-0330 

.09972 

8 

1.9926 

.501866 

I2.O2IO 

5-5348 

.08319 

9 

2.1719 

.460428 

14.1929 

5-9952 

.07046 

10 

2.3674 

.422410 

16.5603 

6.4177 

.06039 

ii 

2.5804 

•387533 

19.1407 

6.8052 

.05225 

12 

2.8127 

•355535 

21-9534 

7.1607 

•04555 

13 

3.0658 

.326179 

25.0192 

7.4869 

•03997 

14 

3-34I7 

.299247 

28.3609 

7.7861 

.03526 

15 

3-6425 

•274532 

32-0034 

8.0607 

•'03125 

16 

3-9703 

.251870 

35-9737 

8.3125 

.02780 

17 

4.3276 

.231073 

40.3013 

8.5436 

.02481 

18 

4.7171 

.211993 

45.0185 

8-7556 

.02221 

19 

5-I4I7 

.194489 

50.1601 

8.9501 

.01994 

20 

5.6044 

.178431 

55-7645 

9.1285 

•01793 

21 

6.1088 

.163697 

61-8733 

9.2922 

.Ol6l6 

22 

6.6586 

.150182 

68.5319 

9.4424 

.01459 

23 

7-2579 

-I3778I 

75.7898 

9.5802 

.01319 

24 

7.9III 

.126405 

83.7009 

9.7066 

.01195 

25 

8.6231 

.115967 

92.3240 

9.8226 

.01083 

26 

9.3992 

.106392 

101.7231 

9.9290 

.00983 

27 

10.2451 

.097608 

111.9682 

IO.O266 

.00893 

28 

11.1671 

.089548 

123.1354 

10.1161 

.008l2 

29 

12.1722 

.082155 

I35-3075 

10.1983 

.00739 

3° 

13.2677 

•075371 

148-5752 

10.2736 

•00673 

31 

14.4618 

.069148 

161-0370 

10.3428 

.00613 

32 

I5-7633 

.063438 

178.8003 

10.4062 

•00559 

33 

17.1820 

.058200 

195.9823 

10.4644 

.00510 

34 

18.7284 

•053395 

214.7108 

10.5178 

.00466 

35 

20.4140 

.048986 

235-1247 

10.5668 

•00425 

36 

22.2512 

.044941 

257-3759 

10.6117 

.00389 

37 

24-2538 

.041230 

281.6298 

10.6530 

•90355 

38 

26.4367 

.037826 

308.0665 

10.6908 

•00325 

39 

28.8160 

•034703 

336.8824 

IO-7255 

.00297 

40 

31.4094 

.031838 

368.2919 

10-7573 

•00272 

4i 

342363 

.029209 

402.  15281  • 

10.7866 

.00248 

42 

37-3I7? 

.026797 

4.39-8457 

10.8134 

.00227 

43 

40.6761 

.024584 

480.5218 

10.8379 

.00208 

44 

44-3370 

.022554 

524.8587 

10.8605 

•  00191 

45 

48-3273 

.020692 

573  1860 

10.8812 

.00174 

46 

52.6767 

.018983 

62^.8628 

10.9002 

.00160 

47 

57-4I76 

.017416 

683.2804 

10.9176 

.00146 

48 

62.5852 

.015978 

745.8656 

10.9336 

.00134 

49 

68.2179 

.014659 

814.0836 

10.9482 

.00123 

50  . 

74-3575 

.013448 

888.4411 

10.9617 

.00113 

OF  LIFE  INSURANCE. 


TABLE  No.  VIII. 
MONETARY  TABLES,  10  PER  CENT. 


N 

Tears. 

Amount  of$i 
in  N  years. 

Present 
Value  of  $i 
due  N  years 
hence. 

Amount  of 
§\per  annum 
in  N  years. 

Present 
Value  o/"$i 
per  annum  for 
N  years. 

Sinking 
fund  that  -will 
amount  to  $i 
in  N  years. 

I 

.IOOO 

.909091 

I.  IOOO 

0.9091 

.90909 

2 

.2IOO 

.826446 

2.3100 

1-7355 

.43290 

3 

•3310 

•75I3I5 

3.6410 

2.6849 

•27465 

4 

.4641 

•683013 

5-I05I 

3.1699 

.19588 

5 

.610^ 

.620921 

6.7156 

3.7908 

.14891 

6 

.7716 

•564474 

8.4872 

4-3543 

.11783 

7 

1.9487 

•5I3I58 

10-4359 

4.8684 

.09582 

8 

2.1436 

.466508 

12-5795 

5-3349 

•07949 

9 

2-3579 

.424098 

H-9374 

5-7590 

.06695 

10 

2-5937 

•385544 

I7-53I2 

6.1446 

•05691 

ii 

2.8531 

•350494 

20.3843 

6.4951 

.04906 

12 

3-1384 

.318631 

23.5227 

6.8137 

.04251 

13 

3-4523 

.289664 

26.9750 

7-1034 

.03707 

14 

3-7975 

•263331 

30-7725 

7-3677 

.03250 

15 

4.1772 

•239392 

34-Q497 

7.6061 

.02861 

16 

4-5950 

.217629 

39-5447 

7-8237 

.02529 

17 

5-0545 

.197845 

44-5992 

8.0216 

.02242 

18 

5-5599 

.179859 

5°-I59l 

8.2014 

.01994 

*9 

6.1159 

.163508 

56.2750 

8.3649 

.01777 

20 

6.7275 

.148644 

63.0025 

8-5136 

.01587 

21 

7.4002 

•I35I30 

70.4027 

8.6487 

.01420 

22 

8.1403 

.122846 

78.5430 

8-77I5 

.01273 

23 

8-9543 

.111678 

87-4973 

8.8832 

.01143 

24 

9.8497 

.101526 

97-3471 

8.9847 

.01027 

25 

10.8347 

.092296 

108.1818 

9.0770 

.00924 

26 

11.9182 

.083905 

120.0999 

9.1609 

.00833 

27 

13.1100 

.076278 

133.2099 

9.2372 

•00751 

28 

14.4210 

•069343 

147.6309 

9.3066 

.00677 

29 

15-8631 

.063039 

163-4940 

9.3696 

.00612 

30 

17.4494 

•057309 

180.9434 

9.4269 

•00553 

31 

19.1943 

.052099 

200.1378 

9.4790 

.00500 

32 

21.1138 

.047362 

221-2515 

9-5264 

•00452 

33 

23.2252 

•043057 

244-4767 

9.5694 

.00409 

34 

25-5477 

•039H3 

270.0244 

9-6086 

•   -00370 

35 

28.1024 

•035584 

298.1268 

9.6442 

•00335 

36 

30.9127 

•032349 

329-0395 

9.6765 

.00304 

37 

34-0039 

.029408 

363-0434 

9-7059 

•00275 

38 

37.4043 

•026735 

400.4478 

9-7327 

.00250 

39 

41.1448 

.024360 

441.5926 

9-7570 

.00226 

40 

45-2593 

.022095 

486.8518 

9.7791 

.00205 

4i 

49.7852 

.020086 

536-6370 

9.7991 

.00186 

42 

54.7637 

.018260 

591.4007 

9.8174 

.00169 

43 

60.2401 

.016600 

651.6408 

9.8340 

•00153 

44 

66.2641 

.015091 

717.9048 

9.8491 

•00139 

45 

72.8905 

.013719 

790-7953 

9.8628 

.OOI26 

46 

80.1795 

.012472 

870.9749 

9-8753 

.00115 

47 

88.1975 

.011338 

959-I723 

9.8866 

.00104 

48 

97.0172 

.010307 

1056.1896 

9.8969 

.00095 

49 

106.7190 

.009370 

1162.9085 

9.9063 

.00086 

5° 

117.3909 

.008519 

1280.2994 

9.9148 

.00078 

LIFE   CONTINGENCIES. 

The  first  fundamental  basis  of  all  life  insurance  calculations  is 
the  law  of  mortality,  or  inversely  the  duration  of  human  life. 
The  age  which  any  individual  will  attain  is  always  a  matter  of 
great  uncertainty,  as  death  in  a  thousand  different  ways  is  liable 
to  take  away  human  life  ;  and  yet  there  is  a  certain  uniform  death 
rate  when  applied  to  a  large  number  of  people  of  any  given  age 
which  would  be  truly  astonishing,  were  it  not  one  of  the  recog- 
nized laws  which  govern  human  affairs.  The  uniformity  of  these 
occurrences,  which  many  regard  as  entirely  fortuitous,  is  one  of 
the  most  interesting  discoveries  of  modern  science.  The  statis- 
tics of  our  fire  insurance  companies  show  that  the  ratios  of  losses 
to  premium  receipts  occur  from  year  to  year  with  surprising 
uniformity  ;  the  aggregate  number  of  suicides  and  murders  annu- 
ally occurring  from  year  to  year  in  a  civilized  country  vary  but 
very  little ;  the  prevailing  direction  of  the  winds  and  the  fall  of 
rain  during  the  corresponding  seasons  of  each  year  display 
almost  uniform  results  in  their  yearly  aggregates.  It  is  on  the 
same  principle,  by  collecting  the  statistics  of  the  deaths  of  a  large 
number  of  persons,  that  the  different  tables  of  mortality  have  been 
formed. 

According  to  the  American  table  of  mortality,  which  is  adopted 
by  the  state  of  New  York,  and  several  other  states,  as  the  official 
standard  for  making  the  valuations  of  the  Insurance  Department, 
out  of  a  class  of  100,000  persons  living  at  the  age  of  10  years, 
92,637  will  be  living  at  20,  85,441  at  30,  78,106  at  40  years  of 
age,  and  so  on  ;  or  the  percentage  of  mortality  in  a  class  of  100,000 
at  the  age  20  is  780 ;  at  30,  843  ;  at  40,  979. 

This  rate  of  mortality  does  not  have  a  uniform  increment ;  but  if 
we  represent  the  probability  of  dying  from  10  to  95  years  of  age  by 
a  line,  it  will  describe  a  curve  very  nearly  the  same  as  a  cycloid. 

The  various  tables  of  mortality,  constructed  in  different  coun- 
tries and  periods,  show  a  great  degree  of  uniformity  in  the  prob- 


OF  LIFE  INSURANCE.  33 

ability  of  life  at  the  same  age ;  and  yet  it  is  an  interesting  and 
encouraging  fact,  that  each  successive  century  is  slowly  length- 
ening the  average  duration  of  human  life.  Improvements  in 
civilization,  more  abundant  supply  of  food,  new  discoveries  in 
medicine,  and  a  more  general  knowledge  of  the  laws  of  physiology 
and  hygiene,  are  having  a  favorable  influence  in  lessening  the  rate 
of  mortality. 

TABLES  OF  MORTALITY. 

The  value  of  life  insurance  calculations  depends  in  a  great 
degree  upon  accurate  and  reliable  tables  of  mortality,  since  it 
is  this  and  the  assumed  rate  of  interest  which  determines  the  net 
premiums,  the  proper  reserves,  and,  to  some  extent,  the  margin 
for  expenses,  and  distribution  of  surplus  to  policyholders.  With- 
out a  reliable  and  well  adjusted  table  of  mortality,  conforming 
very  closely  to  actual  experience,  it  would  be  impossible  for 
these  terms  to  be  correctly  computed,  or  the  policyholders  to  be 
equitably  treated.  It  was  not  till  tolerably  correct  tables  were 
made  that  life  insurance  rose  to  the  dignity  of  a  science.  Pre- 
vious to  this  it  was  all  conjecture.  In  its  early  history  statistics 
of  mortality  were  almost  entirely  neglected.  In  a  few  parishes 
of  England  there  were  registers  of  the  living  and  the  dying,  but 
they  were  so  imperfectly  kept  as  to  be  almost  wholly  unreliable. 
And  the  best  informed  public  men  could  not  tell  whether  the 
population  of  the  country  was  increasing  or  decreasing.  The 
great  truth,  reserved  for  discovery  in  later  times,  that  there  are 
certain  laws  to  which  the  average  duration  of  human  life  con- 
forms, was  never  thought  of.  It  was  for  this  reason  that  when 
life  insurance  companies  were  first  organized  in  England  the 
rates  were  the  same  for  all  ages,  as  the  fees  and  dues  for  co- 
operative associations,  burial  clubs,  workingmen's  unions  and 
friendly  societies  are  at  the  present  day.  But  a  short  period  of 
observation  revealed  the  fact,  which  is  now  regarded  as  self- 
evident,  that  the  aged  are  much  more  likely  to  die  than  the  young, 
and  the  necessity  for  a  different  guide  to  determine  the  probable 
length  of  human  life  became  evident. 

THE  AMERICAN  EXPERIENCE  TABLE. 

This  table,  first  adopted  by  the  state  of  New  York,  in  the  year 
1868,  as  a  basis  for  the  valuation  of  policies,  was  constructed  by 


34 


PRINCIPLES  AND  PRACTICE 


Mr.  Sheppard  Homans,  from  the  experience  of  the  Mutual  Life 
Insurance  Company,  of  New  York,  who  also  availed  himself  of 
other  statistics,  to  ascertain  the  laws  of  mortality  as  applicable 
to  healthy  insured  lives  in  this  country.  All  the  standard  Euro- 
pean tables  were  used  in  adjusting  it.  This  table  of  mortality, 
with  41-2  per  cent  rate  of  interest,  is  now  made  the  legal  standard 
of  valuation  in  several  of  the  states. 

In  the  illustrations  and  explanations  given  in  this  part  of  the 
work,  the  American  Table  of  Mortality  and  4  1-2  per  cent  in- 
terest will  be  used  as  a  basis,  unless  some  other  table  and  rate 
are  expressly  named. 

THE    COMBINED    EXPERIENCE,    OR    ACTUARIES' 

TABLE. 

This  table  was  prepared  by  a  committee  of  eminent  actuaries, 
on  the  data  afforded  by  the  combined  experience  of  seventeen  of 
the  principal  life  insurance  offices  in  England.  It  was  deduced 
from  62,537  assurances,  first  published  by  Mr.  Jenkin  Jones,  in 
1843,  and  furnishes  a  very  accurate  graduation  of  assured  lives. 
Some  of  the  objections  advanced  against  it  are  that  certain  lives, 
having  been  more  than  once, assured,  have  appeared  twice  or 
oftener  as  elements  of  the  calculation,  and  that  the  data  for  the 
older  ages  were  insufficient.  The  mortality  amongst  assured 
females,  taking  all  ages  together,  is  greater  than  amongst  assured 
males.  A  more  careful  comparison  of  the  different  classes  in- 
sured reveals  the  fact  that  the  average  duration  of  male  lives 
under  36  years  of  age  is  greater  than  that  of  females,  and  from 
36  to  6 1  years  of  age  the  average  duration  of  the  lives  of  females 
is  greater  than  that  of  males ;  but  after  the  age  of  61  the  male 
lives  have  a  greater  expectation  than  female  lives.  The  average 
duration  of  all  the  policies  was  a  little  less  than  8  1-2  years. 

RATE   OF  INTEREST. 

The  second  principal  element  of  all  the  calculations  in  life  as- 
surance is  the  rate  of  interest  assumed  by  the  companies  to  be 
realized  on  their  assets.  A  contract  of  insurance  made  between 
the  company  and  the  policyholder  is  designed  to  exist  as  long  as 
the  policy  can  be  continued  in  force,  either  during  a  term  of 
years  or  the  lifetime  of  the  policyholder.  In  contracts  extending 


OF  LIFE  INSURANCE. 


35 


over  a  long  series  of  years,  the  continued  and  ultimate  solvency 
of  the  company  is  of  the  highest  importance,  and  the  adoption  of 
any  erroneous  principles  of  calculation,  and  increased  from  year 
to  year  at  each  renewal  of  the  premiums,  and  moreover  multi- 
plied by  thousands  of  policies  in  force,  cannot  fail  to  work  out  a 
disastrous  result  in  time.  Hence  it  is  of  the  highest  importance 
that  the  primary  elements  of  mortality  and  of  interest  should  be 
such  as  are  perfectly  safe  to  the  insured.  The  company  assumes 
that  the  adopted  rate  of  mortality  will  be  experienced  in  the 
future,  and  m  each  annual  premium  there  is  a  certain  part  set 
aside  or  reserved  to  pay  the  claim  of  the  policyholder  when  it 
becomes  due  ;  and  this  reserve,  according  to  the  laws  and  as- 
sumptions of  life  insurance,  accumulates  at  compound  interest  as 
long  as  the  policy  remains  in  force.  The  question  now  arises, 
what  rate  of  interest  must  be  assumed  as  the  one  which  these  re- 
serves will  earn  during  the  years  that  intervene  between  the  pay- 
ment of  the  first  premium  and  the  final  settlement  of  the  claim  ? 
The  opinions  of  Hon.  Elizur  Wright  on  this  subject  are  worth 
quoting  here : 

"A  very  large  part  of  the  immense  sums  promised  to  be  paid  in  the 
distant  future  is  to  be  produced  by  the  accumulation  of  interest,  and  the 
premium,  being  fixed  at  the  outset  and  unalterable,  it  will  make  a  life 
or  death  difference  with  the  company  whether  six  per  cent  interest  is  al- 
ways to  be  received  on  investments,  or  the  rate  is  to  fall  occasionally  or 
permanently  to  four  or  three  per  cent.  If  the  interest  is  to  be  more,  the 
premium  may  be  less,  and  if  it  is  to  be  less,  the  premium  must  be  more. 
The  only  safety  is  to  assume  a  rate  of  interest  so  low  that  the  profits  on 
investments  may  always  exceed  it,  and  to  divide  at  short  intervals  the 
surplus  that  may  result  from  the  excess." 

"It  is  historically  certain  that  all  experiments  of  life  insurance  that 
have  been  tried  long  enough  to  test  results,  without  reserving  premium 
on  an  assumption  of  interest  lower  than  the  current  interest  on  invest- 
ments, have  proved  failures." — Mass.  Report,  1865,^.  305. 

The  standard  rate  of  interest  adopted  by  the  state  of  New 
York  and  several  other  states,  is  4  1-2  per  cent ;  in  Massachusetts, 
Illinois  and  some  other  states  it  is  4  per  cent. 

PROBABILITY  OF  LIFE. 

The  probability  of  life  is  the  likelihood  which  a  person  has, 
according  to  the  table  of  mortality,  of  living  a  certain  number  of 
years.  The  probability  of  death  is  the  likelihood  a  person  has  of 


36  PRINCIPLES  AND  PRACTICE 

dying  within  a  given  period.  As  it  is  absolutely  certain  that  a  per- 
son will  always  be  dead  or  alive,  the  probability  of  death  is  found 
bv  subtracting  the  probability  of  life  from  unity,  and  vice  versa. 

Example.  Required,  the  probability  that  a  person  aged  thirty 
will  live  to  be  fifty  years  old,  American  table. 

The  number  living  at  the  age  50  is  69,804. 

The  number  living  at  the  age  30  is  85,441. 

Therefore  p^=.8i6gS  the  probability. 

85>44i 
As  there  are  85,441  chances  in  all  of  the  persons  aged  30  at- 

taining to  fifty  years,  and  as  the  probability  is  that  only  69,804 
will  live,  the  contingency  that  each  individual  will  live,  is,  .81698, 
and  hence  the  contingency  of  his  dying  is,  i—  .8  1698=.  18302,  or 

I5»637»  and 


J441 
These  operations  are  sometimes  useful  in  making  estimates 

upon  endowment  policies,  as  to  whether  a  person  will  live  to 
complete  his  payments,  and  on  term  policies,  whether  the  party 
will  die  during  the  period  of  insurance. 

COMMUTATION  COLUMNS. 

The  commutation  columns  are  now  universally  used  in  the 
computation  of  premium  rates,  annuities  and  many  other  cal- 
culations. The  four  principal  columns  are  denoted  by  the  capital 
letters  D,  N,  C,  M.  In  increasing  insurance  S  and  R  are  used. 
The  column  D,  usually  written  D#,  denotes  the  number  of  living 
at  any  age  #,  discounted  by  such  a  power  of  1.045,  or  whatever 
rate  of  interest  is  assumed,  as  corresponds  to  the  age  x.  For  the 

sake  of  convenience  and  uniformity  we  use  that  power  of  - 
which  corresponds  to  the  age  of  the  insured.     It  would  make 

no  difference  in  the  result  if  we  took  the  first  power  of  - 

1.045 

to  discount  the  living  at  the  age  10,  and  the  second  power  for  the 
age  ii,  &c.,  since  the  ratio  between  the  different  numbers  in  the 
column  is  not  changed  by  taking  a  different  exponent  of  discount. 
The  first  number  in  the  column  D  against  the  age  10  is  found  by 
multiplying  100,000,  the  tabular  number  living  at  that  age,  by 

(—  —  V9  or  .64392768,  which  gives  010  =  64392.768.  The 
second  number,  or  Dn,  is  found  by  multiplying  99,251  by 


OF  LIFE  INSURANCE. 


37 


—  —V1  or  .6162087,  which  gives  61158.341.     In  this  manner 

all  the  remaining  terms  in  column  D  are  found.  C  denotes  the 
number  of  dying  at  the  age  x,  discounted  by  the  x+i  power  of 

,  for  the  reason  that  the  deaths  are  computed  as  .taking  place 

at  the  end  of  the  year,  while  the  premiums  are  paid  at  the  begin- 
ning. Thus,  at  the  age  10,  0=749  x  fj-^-)n=749  x . 6162087= 

461.5329,  and  at  the  age  n,  0=746  x  (r^)12=746  x  .58966385= 

439.8892,  and  so  on  with  the  remainder  of  the  column.  The  N 
column  is  found  by  taking  the  sums  of  the  numbers  in  the  D 
column  beginning  with  the  oldest  age,  as  follows :  D  at  the  age 

95=3x(— —  )95= .045822,  and  is  the   same  as  N  at  the  same 

age,  or  N95=.O45822.  N94=D95+D94=.o45822+.335iSS= 
.381010.  N93=D95 +094+093=^4+093=381010+1.317687 
=1.698697.  Continuing  this  process  through  all  the  ages  in  the 
mortality  table,  we  have  the  N  column  complete.  The  M  column 
is  found  by  adding  together  the  terms  of  the  C  column  in  the  same 
manner  as  the  N  column.  The  S  and  R  columns  are  found  by 
adding  together  the  numbers  in  the  N  and  M  column  respectively, 
in  the  same  manner  as  N  and  M  were  obtained  from  D  and  C. 

EXPLANATION  OF  LIFE  INSURANCE. 

The  table  of  mortality  enables  us  to  determine  the  ratio  there 
is  between  the  number  living  at  a  given  age  at  the  beginning  of 
a  year  and  the  number  dying  during  that  year.  At  the  age  30 
there  are  85.441  living,  and  during  that  year  there  are  720  deaths, 
and,  therefore,  the  probability  that  a  person  aged  30  will  die  dur- 
ing that  year  is  «^—  =.0084269.  If  1 ,000  persons  aged  30  insure 

for  $i  each  for  one  year,  the  net  premium  required  of  each,  with- 
out reckoning  interest,  will  be  one  thousandth  part  of  the  total 
losses  at  the  end  of  the  year.  As  the  total  losses  are  8.4269,  the 
net  premium  required  of  each  policyholder  will  be  .0084269. 
But  as  the  premiums  paid  at  the  beginning  of  the  year  are  in- 
creased by  4  1-2  per  cent  interest,  and  the  losses  are  reckoned  to 
take  place  at  the  end  of  the  year,  this  amount  of  premiums  re- 
quired must  be  discounted  at  4  1-2  per  cent,  which  reduces  the 


38  PRINCIPLES  AND  PRACTICE 

total  amount  of  premiums  required  to  $8.0640,  anil  the  amount 
required  to  insure  $i  for  one  year  at  the  age  above  given  is 
.0080640.  At  the  age  31  the  net  premium  for  orfe  year  is 
.0081438,  and  at  32  it  is  .0082365. 

The  foregoing  explanation  relates  entirely  to  temporary  insur- 
ance from  year  to  year,  and,  if  carried  on  through  life,  the  pre- 
mium would  have  to  be  changed  each  successive  year.  In  order 
to  find  the  uniform  annual  premium  required  on  a  policy  payable 
at  death,  and  to  simplify  the  explanation  we  will  take  an  example 
in  which  the  element  of  interest  is  omitted. 

At  the  age  95,  according  to  the  American  Experience  Table 
of  Mortality,  there  are  three  persons  living,  all  of  whom  die 
during  the  year.  Consequently,  if  each  of  these  were  insured  to 
the  amount  of  $i,  there  would  be  three  claims  of  $i  each  to  pay 
during  the  year.  At  the  age  of  94  we  have  21  persons  living, 
18  of  whom  die  during  the  first  year  and  3  during  the  next, 
hence  there  are  21+3  premiums  paid,  and  only  21  claims  to  be 
met;  and,  therefore,  the  amount  of  each  premium  would  be 

—=.875.  At  the  age  of  93  there  are  79  living,  and  the  first  year 
24 

there  are  79  premiums  paid,  the  second  21,  and  the  third  3,  mak- 
ing 103  premiums  to  79  losses,  and  the  annual  premium  to  insure 

$i  is  -^-=.76699. 
103     '     ** 

From  the  above  example  it  will  be  seen  that  the  fundamental 
principle  for  finding  the  premium  to  insure  $i  through  life  for 
any  given  age  (without  regarding  interest)  is  as  follows  :  Divide 
the  number  of  living,  or  future  deaths,  at  any  given  age,  by  the 
total  number  of  premiums  to  be  paid  till  the  death  of  the  last 
survivor. 

It  is  clear  from  the  above  example  that  in  life  insurance  some 
persons  insured  pay  much  more  than  the  company  returns,  and 
others  less.  At  the  age  93  there  are  79  living,  of  whom  58  pay 
.76699  each,  and  the  company  returns  $i  for  each  loss.  At  the 
age  94  there  are  18  claims  of  $i  each,  for  which  18  persons  have 
paid  $1.53398  each  in  two  annual  premiums.  At  the  age  95 
there  are  3  losses  of  $i  each,  on  which  3  persons  insured  have 
each  paid  premiums  amounting  to  $2.30097. 

In  computing  the  net  annual  premium  at  4 1-2  per  cent  interest, 
the  same  general  principles  given  above  are  applicable.  In  the 


OF  LIFE  INSURANCE. 


39 


foregoing  example  we  have  3  persons  living  at  the  age  95.  Ac- 
cording to  the  mortality  table  there  would  be  3  premiums  to  be 
paid  at  the  beginning  of  the  year,  and  3  claims  of  $i  each  at  the 
end  of  the  year  ;  and,  therefore,  the  premium  required  to  insure 
$i  for  one  year  would  be  the  present  value  of  $i  for  one  year,  or 

-  =.9^694. 
1.045     *>  " 

At  the  age  94  there  are  21  living,  and  the  annual  premium  to 
be  paid  is  found  as  follows  : 

Premiums  at  the  beginning  of  the  first  year,     -        -        -        -    21 
Premiums  at  the  beginning  of  the  second  year  discounted= 
3  x  .95694=  2.87082 

Total  premiums  discounted,  -         •....-.    23.87082 
The  next  step  is  to  find  the  present  value  of  the  future  losses. 


Losses  of  the  first  year,  present  value,  i8x  .95694 
Losses  second  year,  present  value,  3  x  .91573= 

Total  losses,  present  value,          -        . 
Annual  premium,  age  94=19.97211  -f- 


17.22492 
2.74719 

$19.97211 


"79 

.    20.09574 
.   2.74719 

-   101.84293 

55-5O2S2 

.    1648314 

-   2.62890 

.   $74.61456 


At  the  age  93  there  are  79  living. 

Premiums  at  the  beginning  of  the  first  year,     -        - 
Premiums  second  year,  21  x  .95694=     ... 
Premiums  third  year,  3  x  .91573=      .... 

Total  number  discounted  premiums,  .        - 

Losses  first  year,  present  value,  58  x  .95694=   - 
Losses  second  year,  present  value,  iSx  .91573=  . 
Losses  third  year,  present  value,  3  x  .87630=   -        - 

Total  losses,  present  value,          ... 
Annual  premium=$74.6i456-f-ioi.84293=.732643. 

In  each  of  the  above  examples  the  number  of  premiums  to  be 
paid  and  the  number  of  losses  to  be  met  are  discounted  by  a 

different  power  of  --  .     It  is  easy  to  see  that  in  computing  pre- 

miums for  the  younger  ages  this  would  be  an  exceedingly  difficult 
anc|  tedious  operation,  were  not  some  more  expeditious  method 
discovered.  The  commutation  columns  enable  us  to  perform 
these  operations  with  much  greater  facility. 

Under  the  head  of  "  Commutation  Columns,"  page  36,  we 
found  that  N  is  the  sum  of  the  numbers  in  the  D  column,  or  the 


40  PRINCIPLES  AND  PRACTICE 

discounted  numbers  of  the  living,  and  M  is  the  sum  of  the  C's  or 
discounted  numbers  of  the  dying.  In  the  last  example  we  have 
the  quantity  101.84293  equals  the  total  number  of  discounted 
premiums,  or  number  of  living  at  the  beginning  of  each  year,  and 
therefore  it  corresponds  to  N93,  discounted  by  a  different  power  of 

— .     The  quantity  74.61456  is  the  discounted  number  of  the 
losses  or  dying  each  year,  and  corresponds  to  M93.     Therefore, 


the  annual  premium  74.61456-*-  ioi.84293=-r=.73264.     And 

generally  the  annual  premium  for  one  dollar  on  a  whole  life 
policy  is  found  by  dividing  the  discounted  number  of  future  losses 
by  the  discounted  number  of  future  premiums  to  be  paid.  Hence 
the  formula  for  finding  the  annual  premium  on  a  whole  life  policy 

M* 

18  ^r- 

N* 

By  referring  again  to  the  commutation  columns,  we  find  that 

-rJ^=—  ^=.77264.  In  the  same  manner  the  net  annual  pre- 
N93  1.698696  /0 

mium  for  the  age  30  is-^T3°=—  ''-7^=.Qi<^6  ;  that  is,  at  the  age 

390642.05       JJO 


30  the  discounted  number  of  future  death  claims,  according  to 
the  table  is  5990.8434,  and  the  discounted  number  of  future  pre- 
miums is  390642.05,  making  the  average  value  of  each  premium 
.015336  on  an  insurance  of  $i.  Hence  the  rule  for  finding  the 
net  annual  premiums  by  means  of  the  commutation  columns  is  : 
Divide  the  discounted  sum  of  the  dying  at  the  given  age  in  the 
M  column  by  the  discounted  sum  of  the  future  premiums  to  be 
paid  as  found  in  the  N  column  at  that  age,  and  multiply  the  quo- 
tient by  the  sum  insured. 

In  the  commutation  columns  N93  is  the  sum  of  the  D's  dis- 

counted by  the  ninety-third,  fourth  and  fifth  power  of  --  -,  and 
die  M  column  is  the  sum  of  the  C's  multiplied  into  one  higher 
power  of  —  —  .  The  reason  why  these  figures  give  the  same  re- 
sult, as  when  we  take  the  living  and  dying  in  the  mortality  table 
and  discount  them  by  the  first,  second  and  third  powers  of  -  ,  is 

that  it  makes  no  difference  in  the  result  what  power  of  —  —  we 

1.045 

use  to  discount  by,  provided  we  take  a  power  higher  by  one  at 


OF  LIFE  INSURANCE.  4! 

each  successive  age.    In  the  first  case  we  have  I  093  x  -  +  C94  x 

In 


i.o45/,  Vi.045/  1-045  Vi.045 

thelatterwe  have  [C93  x  (^)94+C94  x  (I^)M  +  C95  x  (r^)'  '] 


045  /  1-045  /  1-045  /  -      1-045 


(  —  -  —  )     . 
Vi.045/  J 


Since  both  numerator   and   denominator  are 
.045 

/          j          S  g  ; 

multiplied  by  the   same    quantity    f  -  J  '    the   result   is   not 

changed. 

The  net  single  premium  is  the  sum  which,  paid  in  advance, 
will  insure  a  person  during  life.  Were  it  not  for  the  discount 
the  net  single  premium  would  be  equal  to  the  sum  insured  at  all 
ages.  To  find  the  net  single  premium  we  give  the  following 
illustration  :  At  the  age  93  we  have  79  lives  to  insure  in  the  sum 
of  $i  each.  The  present  value  of  all  the  future  annual  premiums 
which  they  would  pay  is  (page  40)  74.61456,  consequently  the 

single  premium  which  would  be  required  of  each  is  —  '       = 

.94449.     Here  the  numerator  represents  MX,  and  we  have  seen 
that  the  denominator  represents  D#;  therefore  the  formula  is 

M#       -r,     ,,  ..  Mg3     1.24415367 

-VT—  .     BV  the  commutation  columns  we  have    -r^=  — 

Dx          J  093      1.317686 

.  ,  .  , 
.94449.     At  the  age 


The  general  rule  given  on  page  40,  for  finding  the  net  annual 
premium  on  a  whole  life  policy,  will  also  apply  to  find  the  annual 
premium  on  a  policy  with  a  limited  number  of  annual  payments. 
A  person  insures  in  the  sum  of  $i  at  the  age  30  on  the  ten  pay- 
ment plan.  The  discounted  number  of  future  claims  at  this  age  is 
5990.8434,  and  the  discounted  number  of  future  premiums  during 
ten  years  from  the  age  30  is  N3<D—  N4o=39o642.O2—  208640.18= 
182001.87  ;  therefore,  if  it  requires  182001.84  premiums  to  meet 
5990.8434  claims  of  $i  each,  what  will  be  the  amount  of  each 
premium?  It  is  evident  that  599O.S434-f-iS2Ooi.84=.O329i6  the 
annual  premium.  Here,  as  before,  we  divide  the  discounted 
number  of  future  claims  by  the  discounted  number  of  future  pre- 
miums to  be  received  during  the  years  in  which  these  premiums 


42  PRINCIPLES  AND  PRACTICE 

are  to  be  paid.     The  formula  for  limited  premium  life  policies  is 
N  _N ,  in  which  n=  the  number  of  years  during  which  the 

annual  payments  are  made. 

In  term  or  temporary  insurance  the  premiums  are  payable 
during  a  limited  number  of  years,  and  the  amount  insured  is  paid 
only  in  case  the  policyholder  dies  during  this  period.  The  pre- 
mium is  the  ratio  which  the  discounted  number  of  premiums  in 
the  column  N,  during  the  period  of  insurance,  bears  to  the  dis- 
counted number  of  claims  in  the  column  M  for  the  same  time, 
and  multiplied  by  the  sum  insured  ;  and  is  found  by  dividing  the 
difference  between  the  number  of  deaths  in  the  M  column,  at  the 
time  when  the  insurance  commences,  and  the  number  when  the 
policy  ceases  to  be  in  force,  by  the  difference  between  the  corres- 
ponding N  numbers  at  the  same  ages.  The  term  insurance  for 
a  policy  of  $i ,  issued  at  the  age  30,  for  ten  years,  is  (M3O— M4o)  -*. 
(N30-N40)  =  (5990.8434-4444. 1 583) -(390642. 05 -208640. 1 8) 
=1546. 6851  —182001. S7=.ooS4982  ;  that  is,  we  assume  that  there 
will  be  1546.6851  deaths  to  182001.87  premiums  paid,  and  there- 
fore each  premium  required  would  be  .0084982. 

Simple  endowment  is  a  form  of  insurance  in  which  the  sum 
insured  is  payable  only  in  case  the  policyholder  is  alive  at  the 
time  when  the  policy  expires  by  limitation.  The  annual  pre- 
mium is  the  ratio  between  the  number  of  payments  made  by  the 
living  during  this  term  and  the  number  living  at  the  end  of  the 
term.  Thus  the  simple  endowment  on  a  person  aged  30,  payable 
at  40,  if  living,  is  the  ratio  between  the  tabular  number  of  pay- 
ments for  ten  years,  commencing  at  30,  and  the  number  of  living 
at  the  age  40,  or  D4O-j-(N3o— N4o)= 13428. 663  —  (390642. 02 — 
2o864o.iS)=i3428.663 -4-182001  .S4=.o737S3.  In  this  example, 
according  to  the  commutation  columns,  the  discounted  number 
of  premiums  to  be  paid  during  ten  years  is  182001.84,  anc^  tne 
discounted  number  of  claims  is  13428.663. 

Simple  endowments  are  very  seldom  issued,  for  the  reason  that 
the  policyholder  assumes  all  the  risk,  and  the  company  is  merely 
a  depository  of  the  premiums  paid.  The  death  of  the  policy- 
holder  allows  the  company  to  retain  all  the  premiums,  and,  as  a 
general  rule,  the  same  amount  of  money  can  be  realized  from  the 
premiums  by  the  ordinary  methods  of  investment.  "  Children's 
endowments"  usually  come  under  this  form  of  so-called  insurance. 


OF  LIFE  INSURANCE.  43 

Endowment  insurance  consists  of  two  parts,  the  simple  endow- 
ment and  term  insurance.  We  have  seen  how  these  are  found 
separately ;  it  remains  only  to  unite  them  in  one  expression.  It 
will  be  noticed  that  in  the  last  two  examples  the  denominators 
are  the  same,  N3O— N4O,  and  that  the  numerators  are  040  and 
MSO— M4O ;  that  is,  the  denominator  comprises  the  discounted 
number  of  premiums  to  be  paid  during  the  ten  years  the  policy 
is  in  force,  and  the  numerator  is  D^o,  the  discounted  number  of 
survivors  at  the  age  40,  and  M/3O— IVfyo,  the  discounted  number 
of  losses  during  the  period  the  policy  is  in  force.  Hence  the 
whole  number  of  claims  divided  by  the  whole  number  of  pre- 
miums gives  the  annual  premium  for  $i  of  insurance.  Carried  out 
by  figures,  the  operation  is  (13428.66  +  5990.8434—4444.1583)-*- 
(390642.05— 208640. 1 8=14975.345  -4-182001.  S3=.o822Si. 

For  an  endowment  insurance  policy  with  a  less  number  of 
premiums  than  the  policy  has  years  to  run,  we  apply  the  same 
principle  as  before,  dividing  the  discounted  number  of  claims  by 
the  discounted  number  of  premiums.  In  a  ten  year  endowment 
policy,  issued  on  a  life  aged  30,  premiums  payable  in  five  years, 
we  have  the  same  numerator  as  before,  040+ M3O—M4O  ;  and  for 
a  denominator,  N3O— N35,  or  (13428.66+5990.8434—4444.1583) 
-*-  (39°642  -°5  -  287677.63) =.14544. 

The  single  premium  in  these  endowments  is  found  by  dividing 
the  numerator,  as  given  above,  by  the  discounted  number  of  living 
in  the  D  column  at  the  age  of  insurance.  Thus  the  net  single  pre- 
mium on  a  ten  annual  endowment  policy  of  $i,  issued  at  the  age 
30,  is  (040 +M30— M4o) -=-030=14975.3451  -=-2281 2. 75=.656446. 

Since  all  premiums  are  simply  the  ratio  of  the  discounted 
number  of  premiums  payable  during  life  or  a  given  number  of 
years  to  the  discounted  number  of  claims  during  the  time  the 
policy  is  in  force,  the  general  rule  for  finding  the  net  premium 
for  any  kind  of  a  policy  is  simply  this :  Divide  the  number  of 
claims,  as  represented  in  the  commutation  columns  during  the 
time  when  the  risk  is  in  force,  by  the  number  of  premiums  during 
the  period  of  their  payment,  and  multiply  the  quotient  by  the  sum 
insured. 

LIFE  ANNUITIES. 

The  duration  of  any  life  annuity  depends  upon  the  existence 
of  the  person  called  the  nominee,  and  according  to  the  American 


44 


PRINCIPLES  AND  PRACTICE 


Experience  Table  of  Mortality  this  must  cease  in  eveiy  case  at  or 
before  attaining  the  age  of  95. 

Let  us  take  847  persons  at  the  age  90,  according  to  the  Ameri- 
can Experience  Table,  and  compute  the  present  value  of  an 
annuity  of  $i  per  annum,  payable  at  the  end  of  the  year,  on  the 
lives  of  each  of  them.  At  the  end  of  the  first  year  385  will  have 
died  ;  hence  the  probability  that  each  person  will  pay  one  dollar 

at  the  end  of  the  year  is  I—  ~  •  =  |  —  .  The  present  value  of  $i 
payable  at  the  end  of  the  year,  at  4  1-2  per  cent  discount,  is 
.956938;  hence  |-^x.956938=.52i97,  the  present  value  of  the 

contingent  payment  of  $i  from  each  of  the  members  living 
at  the  end  of  the  first  year.  The  present  value  of  $i  to  be 
paid  at  the  end  of  the  second  year  by  each  of  the  847  mem- 


Third year,  -|2-  x 
Fourth  year,  —  —  x 

Fifth  year,  g^-x.  802451  =.00284. 

Placing  these  in  a  series,  we  have  for  the  present  value  of 
$i  per  annum,  payable  at  the  end  of  the  year  through  life, 

on  a  person  aged  90  years,  (||x  .956938)  +(g|x  .91573°)  +  (||  x 
.876297  )  +  (  ^x  .838561  )  +  (  g^  x  .802451  )  =.52197+  .23353  + 

.081  73  +  .02079  +  -oo284=.86o86. 

If  the  first  payment  is  to  be  made  at  the  beginning  of  the  first 
year,   it  is  evident  that  the  present  value  of  the  life  annuity  is 

1+86086=1.86086,   and     the   terms    would   read    thus:    —-  + 

047 

—  x  -  +5  —  x(  -  V    etc.     By  inspecting  these  fractions  we 
847    1.045    847    Vi.045/  '  ' 

find  that  the  numbers  847,  462,  216,  etc.,  are  the  numbers  of  the 
living  at  the  beginning  of  each  year,  and,  when  discounted  by 

the  proper  powers  of  --  ,  their  sum  corresponds  to  the  num- 

ber opposite  90  in  the  N  column,  with  this  difference,  that  a 
different  rate  of  discount  is  used,  and  that  the  denominator  847  is 
the  same  as  090  before  it  is  discounted.  Now,  if,  instead  of 


OF  LIFE  INSURANCE.  45 

multiplying  the  numerators  by  the  first,  second,  third,  etc.  pow- 
ers   of   -   — ,  we  multiply  them  by  the  ninety-first,  ninety-second, 
1.045 

ninety-third,  etc.  powers  of and   the  denominator  847  by 

the  ninetieth  power,  the  relative  value  of  these  fractions  will  not 
be  altered,  and  we  shall  have  for  the  denominator,  090  or 
16.12194  and  for  the  numerators  16.12194,  8.415104,  etc.,  or 
090  +  091+092,  etc.  The  sum  of  these  numerators  is  N9O, 

which  is  placed  over  the  denominator  090  thus,  ^-=1.86086= 

the  present  value  of  a  premium  of  $i  per  annum  on  a  person 
aged  90  ;  or,  in  other  words,  the  present  value  of  a  life  annuity  of 
$i  on  a  life  aged  90,  the  first  payment  made  at  the  beginning  of 
the  first  year.  If  the  first  payment  is  made  at  the  end  of  the  first 
year,  leave  out  the  090  from  the  sum  of  the  numerators  and  we 

liave  -jz^=i3.87S7i-5-i6.i2i94=.86oS6.  If  the  first  paymentis 
deferred  for  two  years,  the  present  value  of  the  deferred  annuity  is 
=^-=5.463610-5-16. 1 2i94=.33889.  The  general  expression  for 

Dyo 

an  annuity  is  =y-  and  for  a  deferred  annuity  is  —=: — . 

The  difference  between  the  present  value  of  an  annuity  for 
life  and  the  single  premium  is  this :  The  annuity  is  the  present 
value, of  $i  multiplied  by  the  probability  of  living  at  the  end  of 
each  year,  because  the  annuity  is  payable  only  in  case  the  nomi- 
nee is  living.  Since  all  deaths  are  supposed  to  take  place  at  the 
end  of  the  year,  the  payment  of  each  policy  is  regarded  as  taking 
place  then,  and  hence  the  single  premium  is  equal  to  the  present 
value  of  $i  payable  at  the  end  of  each  year,  multiplied  by  the 
probability  of  dying  that  year.  It  is  evident  that  the  greater  the 
probability  of  dying  the  greater  will  the  premium  be,  while  on 
the  other  hand,  the  greater  the  probability  of  living  the  greater 
the  annuity. 

VALUATION  OF  POLICIES. 

We  have  seen  (page  40)  that  the  net  annual  premium  to 
insure  a  person  aged  30  in  the  amount  of  $i  during  life  is 

^^-=.015336.  If  he  should  postpone  insuring  for  one  year  he 
would  not  save  this  amount,  for  at  the  age  of  31  the  net  annual 


46  PRINCIPLES  AND  PRACTICE 

premium  is  .015787,  and  the  difference  between  these  two  pre- 
miums is  .000451.  By  insuring  at  age  30  he  pays  .000451  less 
premium  every  year  of  his  life,  and  the  present  value  of  this 
is  found  by  multiplying  it  by  the  then  present  value  of  the  life 
annuity  of  $i,  or  .000451x16.9926=00766366.  If  he  should 
postpone  insuring  till  he  reaches  the  age  of  32,  his  net  annual 
premium  will  be  .016265  and  the  difference  between  this  and 
the  premium  at  30  is  .016265  —  oi5336=.ooo929-  Multiplying 
this  by  the  life  annuity  at  age  32,  we  have  .000929  x  16.85573= 
.01565897.  This  is  called  the  net  value  of  the  policy.  If  the 
sum  insured  is  $1.000,  the  net  values  are  $7.66366  and  $15.65897. 
It  is  clear  from  this  illustration  that  if  he  insures  at  the  age  of  30, 
instead  of  deferring  it  one  or  two  years,  he  does  not  lose  all  the 
premiums  he  has  paid.  These  net  values  are  the  same  as  so 
much  ready  money  at  4  1-2  per  cent  interest,  to  be  used  for 
paying  future  premiums.  As  we  proceed  further,  we  shall  find 
that  no  part  of  the  net  premium  is  lost,  strictly  speaking. 

The  net  value  of  a  policy  is  also  found  by  taking  the  differ- 
ence between  the  net  single  premium  at  the  age  when  the  policy 
is  valued  and  the  present  value  of  the  future  net  premiums  to 
be  paid  on  it.  At  age  31,  the  net  single  premium  for  $i  is 
.268261,  and  the  then  present  value  of  all  the  net  premiums  on  a 
life  aged  30  is  the  net  premium  at  30  multiplied  by  the  life 
annuity  at  31  or  .015336  x  16.9926=.  260598,  and  the  difference 
.268261  —  260598=.  007663,  the  net  value. 

The  premium  on  a  policy  of  $i  to  insure  it  for  one  year 
only  at  age  30  is  .008064.  This  is  the  reserve  at  the  beginning 
of  the  year  ;  at  the  end  of  the  year  this  premium  is  entirely 
absorbed  in  carrying  the  annual  risk.  At  the  end  of  six  months 
this  premium  is  half  gone,  and  therefore  the  reserve  is  .008064-1- 


In  the  gross  valuation  of  a  policy  the  present  value  of  the  future 
gross  premiums  receivable  is  considered  as  an  asset,  and  the  pre- 
sent value  of  the  future  net  premiums  taken  at  the  age  of  valua- 
tion as  a  liability.  If  the  latter  is  greater  than  the  former  the 
difference  is  the  gross  value  of  the  policy,  otherwise  there  is  a 
surplus  in  the  hands  of  the  company.  If  the  net  single  premium 
for  $i  at  age  31  is  .268261,  and  the  gross  annual  premium  at 
age  30  is  .0227,  then  the  present  value  of  the  future  gross  pre- 
miums receivable  will  be  .0227  multiplied  by  the  present  value 


OF  LIFE  INSURANCE. 


47 


of  the  annuity  of  $i ,  or  .0227  x  i6.9926=.385732.  The  difference 
between  .385732  and  .268261  is  .1 17471  the  surplus.  That  is,  the 
present  value  of  the  future  receipts  is  .117471  greater  than  the 
present  value  of  the  future  liabilities. 

At  age  40,  multiplying  the  gross  premium  by  the  present 
value  of  the  annuity,  we  have  .0227  x  15.5369— .352688.  But  the 
single  premium  at  age  40  is  .330946,  and  there  is  still  a  sur- 
plus of  .021742.  At  age  50  we  have  the  present  value  of  the 
future  premiums  =  .0227  x  I3.235S=.3OO453,  and  the  net  single 
premium  at  that  age  is  .430037,  leaving  a  gross  value  of 
.129584. 

The  defect  in  this  method  of  valuation  is  that  no  provision  is 
made  for  future  expenses. 

A  modified  form  of  this  method  of  valuation  is  sometimes  prac- 
tised by  taking  off  a  percentage  of  the  gross  premiums  for  ex- 
penses, and  proceeding  as  before. 

AMOUNT  AT  RISK. 

When  a  person  takes  out  a  policy  of  insurance,  the  risk  which 
the  company  assumes  as  liable  to  lose  is  not  the  whole  amount 
insured,  but  the  amount  of  the  policy  less  the  reserve.  For  the 
sake  of  uniformity,  the  reserve  at  the  end  of  the  year  is  taken. 
Hence  the  sum  insured  may  be  divided  into  two  parts,  the  insur- 
ance which  the  company  carries  and  that  assumed  by  the  policy- 
holder.  In  this  last  example  of  a  policy  of  $i  issued  at  age 
30,  it  is  clear  that  the  policyholder  has  a  deposit  in  the  hands 
of  the  company  of  .007663,  thus  insuring  himself  for  this  amount, 
while  the  company  insures  the  balance  or  .992337.  This  is  what 
the  company  would  lose  if  he  should  die  at  the  end  of  the  first 
year.  At  the  end  of  the  second  year  the  risk  which  the 
company  assumes  is  .984341,  and  that  of  the  policyholder 
.015659. 

The  reserve  on  a  policy  when  compared  with  the  amount  at 
risk  is  called  by  Hon.  Elizur  Wright  "  self  insurance,"  since  it  is 
the  unearned  and  unexpended  part  of  the  premiums  which  the 
policyholder  has  on  deposit  in  the  company  to  provide  for  the 
future  payment  of  his  claim.  For  this  reason  Hon.  Gustavus  W. 
Smith,  Insurance  Commissioner  of  Kentucky,  calls  it  the  "trust 
fund  deposit." 

The  amount  at  risk  varies  greatly  in  different  kinds  of  policies, 


48  PRINCIPLES  AND  PRACTICE 

and  it  is  owing  to  the  want  of  a  proper  understanding  of  this 
subject  that  many  people  find  themselves  greatly  mistaken  in 
their  opinions  of  the  benefits  of  short  term  endowments.  Thus , 
a  person  paying  a  premium  on  a  whole  life  policy  of  $1,000  is 
insured  at  the  end  of  each  of  the  first  ten  years  for  $992.34, 
$984-34>  $976-01'  $967-34>  $958-3ri  $948-89'  $939-IQ  $928.91, 
$9l8-33>  $9°7-33  5  average  amount,  $952.09. 

On  a  ten  annual  payment  endowment  for  the  same  age  and  same 
amount  he  is  insured  at  the  end  of  each  year  as  follows :  $921.78, 
$839.42,  $752.69,  $661.34,  $565-11,  $463-7^  $356-83,  $244.16, 
$i  25.34,  $0.00  ;  average  insurance,  $493.04.  That  is  in  a  ten  year 
endowment  a  man  insures  himself  on  an  average  for  more  than 
one-half  of  the  amount  of  the  policy.  The  annual  net  premium  on 
a  ten  annual  endowment  for  this  age  and  amount  is  $82.29,  and 
on  the  whole  life  policy  given  above  $15.34.  On  tne  endow- 
ment plan  as  above  described,  during  the  ten  years  the  policy- 
holder  pays  between  five  and  six  times  as  much  net  annual  pre- 
mium and  gets  only  about  half  the  insurance  as  on  the  whole  life 
plan.  But  there  is  a  partial  offset  to  this,  as  the  premiums  in 
the  former  case  cease  in  ten  years  when  the  amount  insured  is 
paid,  and  in  the  latter  they  may  continue  till  the  policyholder  is 
95  years  old,  according  to  the  assumptions  of  the  American  mor- 
tality table. 

COST  OF  INSURANCE. 

We  have  seen  that  the  amount  at  risk  is  the  sum  insured  less 
the  reserve  at  the  end  of  the  year.  On  an  ordinary  life  policy 
of  $i,  issued  at  age  30,  the  amount  insured  at  the  end  of  the 
first  year  is  .99234.  The  expense  of  insuring  $i  for  one  year 

at  age  30  is    720  =.0084269,  and  therefore  the  cost  of  insuring 
05.441 

.99234  for  one  year  is  .99234  X.oo84269=..oo83623.     This  is  the 
net  cost  of  insurance,  and  is  found  by  multiplying  the  amount  at 
risk  by  the  probability  that  the  insured  will  die  that  year. 

The  cost  of  insurance  at  age  31  is  found  in  the  same  manner. 
Amount  of  policy,      ---------    $i. 

Reserve  at  end  of  second  year,       ...---          0.01566 
Amount  at  risk,          ---------         -98434 

Number  of  dying,  age  31,       -------  721 

Number  of  living,     "          --------         84.721 

Probability  of  dying,  721-7-84721= .0085103 

Cost  of  insurance,  .98434  x  .0085103  ------       .008377 


OF  LIFE  INSURANCE.  49 

The  cost  of  insurance  on  an  ordinary  life  policy  at  age  95  and  on 
an  endowment  insurance  in  the  last  year  of  its  duration  is  nothing, 
because  in  these  cases  the  reserve  equals  the  amount  insured. 

Having  the  net  premiums  and  reserves,  the  cost  of  insurance 
can  be  found  very  easily  by  adding  41-2  per  cent  interest  to  the 
net  premium  and  subtracting  the  reserve,  and  the  remainder  is 
the  cost  of  insurance  for  the  first  year.  For  the  second  and  sub- 
sequent years,  the  cost  of  insurance  is  obtained  by  adding  the 
net  premium  to  the  reserve  of  the  previous  year,  increasing  this 
amount  by  the  interest  and  subtracting  the  reserve  for  that  year. 

In  the  example  above  given — 

First  year — Net  premium,  -....--       .015336 

Interest  4^  per  cent,  .......  .0x30690 

Amount,       --........       .016026 

Reserve  first  year,     -..-..--  .007664 

Cost  of  insurance,         ........       .008362 

Second  year — Reserve  first  year,     ------  .007664 

Net  premium,       ---..-..-       .015336 

Amount,  -....._..          .023000 

Interest  4^  per  cent,      --------      .001035 

Amount,  ---._...-  .024035 

Reserve  second  year,  .......      .015657 

Cost  of  insurance,    --.-...-          .008378 

From  this  view  of  the  subject  we  see  that  there  is  an  actual 
expense  incurred  in  cari»ying  a  risk  in  life  insurance  in  case  the 
policyholder  survives,  since  in  the  example  above  given  the  720 
losses  which  occur  at  the  age  30  must  be  met  by  the  85,441 
premiums,  and  in  this  respect  life  insurance  adopts  the  same 
law  which  runs  through  all  other  kinds  of  insurance.  At  any 
age  the  greater  the  reserve  the  less  the  cost  of  insurance,  and 
conversely.  In  the  case  of  a  whole-life  policy  issued  at  age 
30,  the  'cost  of  insurance  during  the  first  year  of  issue  is  greater 
than  the  reserve,  and  therefore  a  company  would  not  be  justified 
in  paying  a  surrender  value  of  even  one-half  the  net  premium, 
while  in  a  ten-payment  endowment  it  could  return  nearly  the 
whole. 

DISTRIBUTION  OF  SURPLUS. 
Having  explained  the  method  of  finding  the  reserve  and  the 


50  PRINCIPLES  AND  PRACTICE 

cost  of  insurance,  we  are  now  prepared  to  examine  the  methods 
of  distributing  the  surplus. 

The  method  of  distribution  now  almost  universal  in  this 
country  is  called  the  "  Contribution  Plan,'l  because  it  returns  to 
each  policyholder  the  amount  of  surplus  contributed  by  him. 

There  are  three  sources  of  surplus,  and  each  of  these  will  have 
to  be  considered  separately.  There  is  a  surplus  from  loading, 
when  this  is  greater  than  the  expenses,  or  the  expenses  and 
mortality,  over  the  tabular  rate.  If  the  loading  on  ordinary  life 
policies  is  40  per  cent  and  the  average  expense  is  but  15,  we 
have  a  surplus  of  25  per  cent  on  the  net  premium  to  return  to  the 
policyholder.  The  second  source  is  from  excess  of  interest.  If 
the  tabular  rate  of  interest  on  reserves  is  4  1-2  per  cent,  and  the 
actual  rate  of  interest  on  assets  is  6  1-2,  then  here  is  a  gain  of  2 
per  cent  on  the  reserves,  and  a  further  gain  of  6  1-2  per  cent  on 
that  part  of  the  loading  not  taken  for  expenses.  The  third  source 
is  from  diminished  mortality.  If  the  actual  mortality  during  the 
year  does  not  equal  the  tabular  mortality,  the  difference  is  so  much 
gained  and  goes  to  swell  the  surplus  ;  but  if,  on  the  other  hand,  it 
is  greater,  then  its  deficiency  must  be  made  up  from  the  loading. 

The  arithmetical  explanation  of  this  plan  will  be  best  under- 
stood by  taking  the  example  of  a  whole-life  policy  for  $1,000, 
issued  at  age  30 ;  gross  premium,  $22.70.  We  will  assume  that 
the  experience  of  the  company  at  the  end  of  each  year  shows 
that  the  expenses  are  15  per  cent  of  the  gross  premiums,  that  the 
average  rate  of  interest  realized  is  6  i«2  per  cent,  and  that  the 
mortality  is  only  three-quarters  of  the  tabular  rate.  The  three 
sources  of  surplus  will  be  as  follows  : 

First  Source — From  loading, 

Gross  premium,         -----.... 
Net  premium,        ----..--- 

Loading,  -----------    $7.36 

Expenses  $22.70  x  15=  -.-.---•         3.41 

Difference,         ..------..    $3.95 

Interest  at  6.^  per  cent,  -------  .j- 

Surplus  from  loading,       ------._    $4.20 

Second  Source — Interest  on  reserves. 

Reserve  at  end  of  first  year,  ----..        $7.66 

Difference  between  the  actual  and  assumed  rate  of  interest  2 

per  cent  x  $7.66=  -         -         -         -         -         -         -         -         .15 


OF  LIFE  INSURANCE,  51 

Third  Source — Cost  of  insurance,        ------        $8.39 

Gain  of  one-fourth,        --------      2.09 

Total  surplus  $4.20 +  .15 +  $2.09=  ...  6.44 

SECOND  YEAR. 

First  Source — Surplus  from  loading  same  as  before,     -        -        -    $4.20 
Second  Source— Interest  on  reserves,  $15.66  x. 02=  -        -  .31 

O   -Q 

Third  Source — Gain  from  mortality  -L—  =  ....       2.09 

Total  surplus,      ---          ...-_-        $6.60 

This  method  of  distributing  the  surplus  can  also  be  illus- 
trated by  opening  a  debit  and  credit  account  with  the  policy- 
holder  :* 

Cr. — Gross  premium,        --------        $22.70 

Interest  on  net  premium,  4^  per  cent,         ...        -  .68 

Interest  on  loading,  6^  per  cent,      ------      .25 

Surplus  interest  on  reserves,  2  per  cent,       -         -         -         -          .15 

Gain  from  mortality,        --------    2.09 

$25.87 

Dr.— Reserve,     ----------  $7.66 

Expenses,       ----------  3.41 

Cost  of  insurance,  table  rate,   ------  8.36 

Dividend  to  balance,    -------.  6.44 

$25.87 

This  explanation  shows  that  the  policyholder  is  credited  with 
all  the  contributions  he  makes  and  is  charged  with  only  the  nec- 
essary expenses,  mortality  and  reserves.  What  remains  after 
these  deductions  belongs  to  him. 

By  adding  the  net  premium  and  interest  together,  $15.34+ 
.68=$  16.02,  we  have  the  reserve  and  cost  of  insurance  =  $7. 66  + 
$8.36=$i6.o2,  which  explains  the  presence  of  the  .68  interest 
in  the  above  credit  account. 

The  principal  objection  to  the  contribution  plan  is  that  under 
certain  circumstances  it  shows  a  deficiency  in  the  assets.  If 
a  deficiency  actually  exists,  it  would  be  difficult  to  show  a 
surplus.  To  illustrate  how  the  plan  operates  in  case  of  a  defi- 
ciency, take  the  example  of  a  whole-life  policy  of  $1,000,  age 

*  For  this  illustration  I  am  indebted  to  my  friend,  Mr.  Henry  W.  Smith, 
Actuary  of  the  Hope  Mutual  Life  Insurance  Company,  of  New  York. 


53 

30,  annual  premium  $16.55,  no  gains  from  favorable  mortality, 
and  the  account  will  stand : 

Cr. — Gross  premium,       -.-...-        $16.55 
Surplus  interest  of  2  per  cent  on  actual  reserve  of 

$6.52, .13 

Interest  on  net  premium  ------  .68 

Total,  $17.36 

Dr. — Reserve  required  by  law,          -----        $7.66 

Cost  of  insurance,         -------       8.36 

Expenses,  15  per  cent,      ------  2.48 

Total, $18.50 

Balance  against  the  company,      -        -        -        -  1.14 

Here  is  a  difference  of  $1.14,  which  equals  the  difference  be- 
tween the  actual  and  the  required  reserve,  $7.66— $6. 52=$!.  14. 

There  are  other  methods  of  distributing  surplus,  such  as  the 
percentage  plan,  by  a  percentage  on  the  gross  premiums,  or 
a  percentage  on  the  reserves,  or  on  the  amount  insured ;  and 
they  are  so  simple  as  to  require  no  particular  explanation.  But 
none  of  these  can  be  adapted  to  different  kinds  of  policies  and  to 
premiums  with  different  percentages  of  loading,  and  make  an 
equitable  adjustment  of  surplus,  like  the  contribution  plan. 

Surplus  may  be  applied  in  several  different  ways  to  benefit  the 
policyholder,  but  they  may  all  be  reduced  to  two  :  the  reduction 
of  premium,  and  the  increase  of  insurance.  It  may  be  deducted 
from  the  next  premium,  the  policyholder  paying  the  difference, 
or  it  may  be  applied  to  the  permanent  reduction  of  the  premium 
in  the  following  manner  :  Divide  the  surplus  by  the  present  value 
of  an  annuity  of  $i  at  the  present  age  of  the  policyholder.  If  a 
man  aged  50  has  a  surplus  of  $100  on  a  continued-payment  life 
policy,  divide  $100  by  13.2358,  the  present  value  of  $i  at  age 
50,  and  the  result  is  $7-5553,  the  annual  reduction.  To  find 
what  would  be  the  temporary  reduction  for  ten  years,  we  have  the 
present  value  of  a  temporary  annuity  of  $i  for  ten  years,  which  is 

N*~P*+        =  A5o.io  =7.7393  and  $ioo-*-7.7393=$i2.92i.     To 

find  how  much  this  surplus  will  give  a  permanent  increase  to  the 
policy,  taking  the  net  premium  as  a  basis,  we  have  the  ratio,  if 
.43037  will  purchase  $i  insurance,  $100  will  purchase  $100-5- 
.43037 =$23 2. 538  ;  that  is,  we  divide  the  surplus  by  the  single 


OF  LIFE  INSURANCE. 


53 


premium  of  $i  for  the  given  age.  The  temporary  increase  of 
the  policy  for  ten  years  is  found  by  dividing  the  surplus  by  the 
single  premium  of  $i  for  ten  years,  or 


TONTINES  AND  TONTINE  DIVIDENDS. 

Tontines  are  a  kind  of  life  annuity  which  were  first  brought 
into  public  notice  in  Europe  by  Lorenzo  Tonti,  a  Neapolitan,  in 
the  year  1648.  The  members  of  a  tontine  were  divided  into 
classes  according  to  their  ages,  and  each  individual  subscribed 
a  certain  sum  which  was  invested  so  as  to  produce  an  annual 
revenue  to  be  divided  among  the  survivors.  Each  succeeding 
year  the  numbers  of  the  living  became  less  and  the  revenue  was 
concentrated  upon  a  smaller  number  of  survivors  until  the  last 
one  passed  away,  when  the  capital  subscribed  reverted  to  the 
crown. 

The  first  association  of  this  kind  in  France  was  founded  in 
1653,  under  the  administration  of  Cardinal  Mazarin,  and  called 
the  "Royal  Tontine."  The  total  sum  subscribed  was  1,025,000 
francs,  and  the  members  were  divided  into  ten  classes  paying 
102,500  francs  each.  Each  individual  subscription  was  300 
francs  and  the  subscriber  received  the  interest  on  this  sum  which 
was  annually  increased  by  the  dividend  arising  from  the  sub- 
scriptions of  other  members  who  had  died  during  the  year. 
In  France  in  1726,  a  widow,  the  last  surviving  member  of  a 
tontine  died  at  the  advanced  age  of  ninety-six.  She  had  been 
the  wife  of  a  poor  surgeon  who  had  invested  her  little  capital  of 
300  francs  in  a  tontine,  and  at  her  death  she  enjoyed  a  revenue 
of  795000  francs. 

The  Tontine  Association  of  New  York  was  established  in 
1794  by  several  prominent  merchants  of  that  city,  who  were  desi- 
rous of  having  an  exchange  where  they  could  meet  and  trans- 
act business.  They  formed  a  Tontine  Association  and  issued 
203  shares  of  stock  valued  at  $200  each,  and  with  this  fund, 
amounting  to  $40,600,  they  purchased  a  piece  of  property  on  the 
corner  of  Wall  and  Water  streets  and  erected  a  building  known 
as  the  Tontine  Coffee  House.  The  members  of  the  association 
agreed  that  each  could  nominate  some  one  person  during  whose 
life  the  interest  in  the  funds  would  be  paid,  and  in  most  cases 
the  nominees  were  their  own  or  a  friend's  children.  By  a  recent 


54 


PRINCIPLES  AND  PRACTICE 


arrangement,  it  was  agreed  by  the  'surviving  members  that 
when  their  number  should  be  reduced  to  seven  the  property 
would  be  divided  among  them  and  the  old  Tontine  Associa- 
tion be  brought  to  ,a  close.  The  members  having  been 
reduced  by  death  to  the  required  number  in  1870,  the  preliminary 
steps  were  taken  to  have  the  property,  amounting  to  $300,000, 
divided  among  the  survivors. 

Life  insurance  and  tontines  are  opposed  to  each  other  in  the 
advantages  which  they  offer.  In  the  former  the  gain,  if  we  may 
use  the  expression,  is  on  the  part  of  him  who  dies  early,  and  the 
earlier  the  policyholder  dies  the  greater  is  the  amount  of  insur- 
-ance  obtained  on  a  given  kind  of  policy.  In  the  tontine  the 
advantage  is  altogether  on  the  side  of  him  who  survives  the 
longest. 

To  illustrate  the  nature  of  tontines,  we  will  suppose  that 
69,804  persons  at  the  age  of  fifty,  contribute  one  dollar  each  at 
the  beginning  of  each  year  to  form  a  tontine  fund,  and  this  to  be 
equally  divided  among  the  survivors,  at  age  60.  If  the  money 
is  placed  at  compound  interest,  7  per  cent,  and  the  mortal- 
ity is  the  same  as  the  American  Experience  Table,  the  follow- 
ing will  be  the  result : 

Living  at  the  beginning  of  ist  year     -        -      69,804x1.9672=137.318.10 

4  4<                 2d  "  -  68,842x1.8385=126,566.01 

4  "                3d  "  67,841x1.7282=116.564.42 

'  "                 4th  "  -         66,797x1.6058=107,262.65 

4  "                  5th  "  65,706x1.5007=98,605.00 

4  "                 6th  "  -         64.563  x  1.4026=  90,556.06 

4  "                7th  "  63,364x1.3108=83,057.54 

4  "                8th  "  -         62.104x1.2250=76,077.40 

4  44                 gth  "  60,779x1.1449=69,585.89 

4  "  loth  "  59>3S5  x  1-07     =63,541.96 

Total  amount  to  be  distributed     ------      $969: 135.03 

Survivors  at  the  end  of  the  tenth  year,  ...  57>9i7 

Share  of  each  surviving  member,         -----  $16.73 

Amount  of  $i  per  annum  at  7  per  cent  compound  interest  for 

ten  years         ---------  $14.78 

Gain  from  the  tontine  system  -----  $1-95 

The  application  of  the  tontine  principle  to  the  distribution  of 
surplus  or  bonus  in  life  insurance  companies  has  long  been  the 
subject  of  practical  and  scientific  investigation  in  England,  and  in 
a  modified  form  it  has  been  adopted  by  several  companies  in  this 


OF  LIFE  INSURANCE. 


55 


country.  All  the  different  methods  of  applying  dividends,  in 
which  the  main  idea  is  to  defer  them  for  a  number  of  years,  and 
then  tojsay  them  to  those  policyholders  only  who  have  persisted 
in  keeping  their  policies  in  force  usually  for  ten  or  more  years, 
while  all  the  premiums  and  surplus  of  those  who  have  allowed 
their  policies  to  lapse,  or  who  have  died,  is  concentrated  upon 
those  policies  which  remain  in  force,  involve  the  principle  of  the 
tontine  system.  Considering  the  large  number  of  policies  which 
lapse  after  one  or  two  premiums  are  paid,  and  the  prospect 
there  is  of  realizing  a  much  larger  dividend  than  by  the  ordinary 
method,  it  is  not  strange  that  this  feature  should  have  some 
attractions,  for  those  who  can  afford  to  assume  the  risk  that  they 
will  live  to  enjoy  its  benefits. 

EXPECTATION  OF  LIFE. 

"  The  Expectation  of  Life  expresses  the  true  average  duration 
in  years  of  a  certain  number  of  individuals  at  a  certain  age."  — 
Neison. 

The  calculation  of  a  life  expectancy  is  very  simple.  In  the 
American  Experience  Table  of  mortality,  at  age  95,  there  are 
3  living  at  the  beginning  of  the  year,  and  all  die  during  the 
year  ;  and,  therefore,  assuming  that  the  deaths  of  each  year  are 
equally  distributed  throughout  that  year,  we  have  the  average 
expectation  of  these  3  persons  to  be  half  a  year  each,  or  .50,  and 
the  number  of  years  which  the  aggregate  of  these  three  lives  will 
amount  to  will  be  1.50.  At  the  age  94  there  are  21  living  at  the 
beginning  of  the  year,  and  18  dying  during  the  year.  The  18 
who  die  during  the  year  live  in  the  aggregate  9  years,  and  there 
are  3  who  live  during  the  whole  of  this  year  and  half  of  the  next, 
making  the  total  number  of  years  lived  by  these  21  to  be 
9  +  3  +  1.50=13.50,  and  this  divided  by  21  =.64,  the  expectation. 
For  the  age  93  we  have  79  living  and  58  deaths  during  the  year. 


Hence,  (  f  +  21  +  13.50)  -79=63.5o-79=.So,  or|  +  (  ~3  )  =.8o. 

T>  i      /2i6  +  79  +  4i+3\  319 

ror   age    01    we    have     •+(-  —  -}=.^o+—^=i,ig. 

2     \          462          /     J       462 


To  find  the  expectation  of  life  for  any  age  we  have  the  follow- 
ing rule  : 

Divide  the  sum  of  tH<*  tabular  numbers  of  the  living  at  all  the 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  IX. 
EXPECTATION  OF  LIFE  BY  DIFFERENT  TABLES. 


4 

-k  5 

«l 

Carlisle. 

t*5 

>M 

£$ 
4_ 

Combined 
Experience. 

American 
Experience. 

\ 

«5 

«! 

Carlisle. 

fO 

«5 

!« 

Combined 
Experience. 

American 
Experience. 

i 

32-74 

44.67 

46.65 

53 

6-54 

18.97 

17.67 

18-16 

18.79 

2 

7*7   *7O 

An   r  r 

48  ST. 

CA 

ft  ofi 

18.28 

1  7.06 

TH    ro 

1  8  OQ 

o/-/y 

7O    CC 

4/-OO 

Af\    8? 

iJ.U.0^ 

AT\  61 

i4 

rr 

J.W.VAJ 

c  c8 

T»7   eg 

lf\  A  r 

17".SU 

1  6.  86 

T  *7    /1O 

oy-oi 

/to  c8 

T-y-01 

CO  Tfi 

mj.\ji 

A.Q  8  1 

03 

c6 

5-5° 

5    TO 

1/-;>o 
16-89 

lu-4o 
1C.  86 

16.22 

i  /-4<J 
16.72 

T-w.^o 
40.84. 

ilj-/u 
r  T    'j  ^ 

Ty."-11 

Ac\  *7T 

ou 

C*7 

.1U 
A    £\1 

16.2  1 

Ij'W 
T  C    96 

T  C    CO 

T  f\   OC 

6 

AT    O*7 

O1"'4 

c,  i  .  1  6 

T-y-/1 

AO   7O 

57 
c8 

14.03 

4T   r 

T  C    CC 

l^.^VJ 
14.68 

15-59 

HO7 

iu-uO 

T  C    7O 

rj 

T1>u/ 

AT   O7 

CO  *7O 

T^y-oy 

J.8  Q2 

5° 

CO 

'X5 

T-J   AC 

^D'OD 
T/l  O2 

14.  10 

•y/ 

T  A    7*7 

15-o9 

TA  nA_ 

I 

8 

T1>UO 

^o  *7n 

ou-/y 

CO  7^ 

^<j.y- 
4.8  7.7 

60 

Ij.UO 
1    *>  T 

1T-y-i 

HI  A 

T  *2    C7 

14.J/ 

T  7    ^7^7 

14-/4 

T  A  on 

9 

4u-79 
40-36 

o°'^4 

49-57 

T-°-O/ 

47-74 

61 

13.21 
12.74 

•o4 
13.82 

16-56 
12.96 

13-77 
13.18 

14.09 
13-47 

10 

39-78 

48.82 

47-05 

48.36 

48.72 

62 

12.28 

I3-3I 

12.41 

12.  6l 

12.86 

II 

39-  H 

48.04 

46.31 

47-68 

48.08 

63 

II.81 

12.  8-1 

11-87 

12.05 

12.26 

12 

38.49 

47.27 

45-54 

47-01 

47-44 

64 

"•35 

12.30 

H-34 

11.51 

11.68 

13 

37.83 

46.50 

44.76 

46.33 

46.82 

65 

10.88 

11.79 

10.82 

10.97 

II.IO 

H 

37-17 

45-74 

43-97 

45-64 

46.16 

66 

10.42 

11.27 

10.32 

10.46 

10.54 

15 

36.51 

44.99 

43.18 

44.96 

45-50 

67 

9-95 

10.75 

9-83 

9.96 

10.00 

16 

35-85 

44.27 

42.40 

44.27 

44-85 

68 

9-50 

10.23 

9-36 

9-47 

9.48 

»7 

35-20 

43-57 

41.64 

43.58 

44.19 

69 

9-05 

9.70 

8.90 

9.00 

8.98 

18 

34-58 

42.87 

40.90 

42.88 

43-53 

70 

8.60 

9.15 

8-45 

8-54 

8.48 

19 

33-99 

42-16 

40.17 

42.19 

42.87 

7i 

8.17 

8.6c. 

8.03 

8.10 

8.00 

20 

33-43 

41.46 

39-48 

41.49 

42.20 

72 

7-74 

8-16 

7.62 

7.67 

7-54 

21 

32.90 

40-75 

38.80 

40.79 

41-53 

73 

7-32 

7.72 

7.22 

7.26 

7.10 

22 

32-39 

40-03 

38-13 

40.09 

40-85 

74 

6.92 

7-33 

6.85 

6.86 

6.68 

23 

31-87 

39-31 

37-46 

39-39 

40.17 

75 

6-54 

7.00 

6-49 

6.48 

6.28 

24 

3I-36 

38-58 

36-79 

38.68 

39-49 

76 

6.18 

6-69 

6.15 

6.11 

5-88 

25 

30-85 

37-86 

36.12 

37-98 

38-81 

77 

5.83 

6-40 

5-82 

5-76 

5-48 

26 

30-33 

37-J3 

35-44 

37-27 

38.11 

78 

5-48 

6.11 

5-5i 

5-42 

5.10 

27 

29.82 

36-40 

34-77 

36-56 

37-43 

79 

5-u 

5.80 

5.21 

5-09 

4-74 

28 

29.30 

35-68 

34.10 

35-86 

36-73 

80 

4-75 

5-5i 

4-93 

4.78 

4-38 

29 

28.79 

34-99 

33-43 

35-15 

36-03 

81 

4.41 

5-20 

4.66 

4.48 

4.04 

30 

28.27 

34-34 

32-76 

34-43 

35-33 

82 

4-09 

4-93 

4.41 

4.18 

3-7i 

V 

27-75 

33-68 

32-09 

33-72 

34.62 

83 

3-8o 

4-65 

4.17 

3-90 

3-39 

32 

27.24 

33.02 

31.42 

33-oi 

33-92 

84 

3.58 

4-39 

3-95 

3-63 

3.08 

33 

26.72 

32-36 

30-74 

32-30 

33-21 

85 

3-37 

4-13 

3-73 

3-36 

2-77 

34 

26.20 

3i-68 

30.07 

3I-58 

32-50 

86 

3-i8 

3-9° 

3-53 

3.10 

2-47 

35 

25.68 

31-00 

29.40 

30-87 

3I-78 

87 

3-oi 

3-7i 

3-34 

2.84 

2.19 

36 

25.16 

30-32 

28-73 

30-15 

31-07 

88 

2.86 

3-40 

3.16 

2-59 

i-93 

37 

24.64 

29.63 

28.06 

29.44 

30-35 

89 

2.66 

3-47 

3-00 

2-35 

1.69 

38 

24.12 

28.95 

27-39 

28.72 

29-62 

90 

2.41 

3.28 

2.84 

2.  II 

1.42 

39 

23-60 

28-27 

26.72 

28-00 

28-90 

9i 

2.08 

3.26 

2.69 

1.89 

1.19 

40 

23.07 

27.61 

26.06 

27.28 

28-18 

92 

i-75 

3-37 

2-55 

I67 

.98 

4i 

22.56 

26.97 

25-39 

26.56 

27-45 

93 

i-37 

3-48 

2.41 

1.47 

.80 

42 

22.04 

26.34 

24-73 

25-84 

26-72 

94 

1.05 

3-53 

2.29 

1.28 

.64 

43 

21-54 

25-7i 

24.07 

25.12 

25-99 

95 

•75 

3-53 

2.17 

1.  12 

•50 

44 

21.03 

25.09 

23.41 

24.40 

25-27 

96 

•5° 

3-46 

2.06 

•99 

.... 

45 

20.52 

24-45 

22.76 

23.69 

24-54 

.... 

3.28 

i-95 

.89 

.... 

46 

20.02 

23.81 

22.11 

22.97 

23-80 

98 

.... 

3-°7 

1-85 

•75 

.... 

47 

19-51 

23.17 

21.46 

22.27 

23-08 

99 

.... 

2-77 

1.76 

•50 

.... 

48 

19.00 

22.  SO 

20.82 

21.56 

22.36 

100 

.... 

2.28 

1.68 

.... 

.... 

49 

CO 

18.49 

T  *7  r\r\ 

2I.8I 

*)  T     T  T 

20.17 

T  f\    C  A 

20.87 

90   T& 

21-63 

2O*QI 

IOI 

1  02 

.... 

1.79 

.... 

.... 

.... 

5° 

si 

17.99 
17-50 

i  tj  r\'j 

^  i.  •  1  1 

20.39 

1r\  fiS 

I9-54 
18.90 

TC   --,0 

—  (J.  1  O 
19.50 
T<3    8l 

20.20 

T  C\    Af\ 

103 

VC\A 

87 

"* 

i  f  *\j& 

1U.UO 

1O.  ^O 

1  O*  O<£ 

19.49 

•W« 

OF 


INSURANCE. 


57 


ages  greater  than  the  given  age  by  the  given  age,  and  increase 
the  quotient  by  one-half. 

The  expectation  of  life  is  never  used  in  any  exact  calculations 
in  life  insurance,  but  it  is  often  referred  to  for  the  sake  of  making 
off-hand  estimates  on  the  probable  duration  of  a  lifetime.  Its 
want  of  adaptation  to  the  computation  of  premiums  is  easily 
illustrated  by  the  following  table  : 

TABLE  No.  X. 


A. 

B. 

c. 

D. 

E. 

4f<. 

Expectation 
of  Life. 

Net  Annual  Pre- 
mium, $1.000. 

Amount  o/"$i.oo, 
per  Annum  during 
Expectation,  45 
per  cent. 

Net  Annual  Pre- 
mium, multiplied  bv 
Annuity  =  C  x  D. 

IO 

49 

9-973 

I77-5030 

1770.19 

15 

46 

10.843 

152.6726 

I655-50 

20 

42 

11.065 

124.2764 

1487.08 

25 

39 

13-423 

106.0303 

1423.29 

30 

35 

I5-336 

85.1640 

1306.07 

35 

32 

17.877 

71.7562 

1282.75 

40 

28 

21.301 

56.4230 

1201.84 

45 

25 

25.986 

46.5706 

I2IO.2O 

50 

21 

32.490 

35-3034 

1146.99 

55 

17 

4I-527 

25-855I 

1073.68 

60 

14 

54-I4I 

19.7841 

1071.13 

65 

II 

71.898 

14.4640 

1039-93 

Column  A  gives  the  age  of  the  insured,  B  the  expectation  in 
even  years,  C  the  net  premium  for  $1,000  on  the  whole  life  rate, 
D  the  amount  of  $i  per  annum  at  4  1-2  per  cent,  and  E  the  net 
premium  multiplied  into  the  amount  of  $1.00  per  annum,  or 
C  x  D.  If  the  sum  insured  were  equal  to  the  net  premium  mul- 
tiplied by  the  amount  of  $i  per  annum  during  expectation,  as 
many  people  suppose,  then  the  amounts  in  the  last  column 
would  be  $1,000  each,  whereas  they  vary  from  it  by  considerable 
differences. 

EQUATION  OF  LIFE. 

This  is  a  term  used  by  Mr.  T.  G.  P.  Neison  to  represent  the 
number  of  years  for  which  there  is  an  equal  probability  of  living, 
and  which  he  regards  as  the  best  mode  to  determine  the  com- 
parative value  of  life  within  this  period,  as  the  expression  is 
affected  by  the  mortality  within  these  years  only.  The  expecta- 
tion of  life,  which  is  often  confounded  with  a  chance  of  living  an 
equivalent  number  of  years,  merely  expresses  the  true  average 
duration  in  years  of  a  class  of  individuals  at  a  certain  age  :  it 


PRINCIPLES  AND  PRACTICE 


involves  a  consideration  of  the  decrements  of  life  at  every  superior 
age,  and,  consequently,  at  even  younger  ages,  it  is  affected  by 
the  irregularities  of  mortality  at  the  older  ages. 

The  equation  of  life  is  illustrated  by  the  following  example: 
At  age  20,  according  to  the  American  Experience  Table  of 
mortality,  there  are  92,637  persons  living,  and  the  equation  of 
life  represents  the  period  when  one  half,  or  46,318,  will  be  sur- 
viving. At  age  66  there  are  47,361  alive,  and  the  difference 
between  these  two  numbers,  47,361—46,318=1043;  hence  the 
equation  will  fall  between  the  ages  66  and  67.  The  number 
dying  between  these  ages  is  2,070 ;  hence  we  have  the  proportion, 
^,070  : 1,043  : :  I :  .50  ;  that  is,  the  equation  of  life  will  be  reached 

TABLE  No.  XI. 
EQUATION  OF  LIFE. 


Age. 

Amer- 
ican Ex- 
perience. 

Com- 
bined Ex- 
perience. 

^ 

Amer- 
ican Ex- 
perience. 

Com- 
bined Ex- 
perience. 

Affe. 

Amer- 
ican Ex- 
perience. 

Com- 
bined Ex- 
perience. 

10 

54-65 

53-34 

40 

29.79 

28.47 

70 

7-86 

7-75 

II 

53-85 

52-52 

41 

28.96 

27.64 

71 

7-38 

7.29 

12 

53-05 

51.69 

42 

28.12 

26.83 

72 

6.91 

6.86 

13 

52-23 

50-87 

43 

27.28 

26.O2 

73 

6.48 

6-44 

H 

51.42 

50.06 

44 

26.46 

25.21 

74 

6.0^ 

6.04 

15 

50.6l 

49-23 

45 

25.62 

24.40 

75 

5-65 

5-66 

16 

49-79 

48-38 

46 

24.79 

23-59 

76 

5-26 

5-30 

*7 

48.98 

47-55 

47 

23-97 

22.80 

77 

4-87 

4-96 

18 

48.15 

46.72 

48 

23-I4 

22.  OI 

78 

4-5i 

4.64 

19 

47-33 

45-89 

49 

22-33 

21.23 

79 

4.16 

4-33 

20 

46.50 

45.06 

50 

21.52 

20.46 

80 

3-83 

4-03 

21 

45-68 

44.22 

5i 

20.72 

I9.70 

81 

3-52 

3-77 

22 

44-85 

43-39 

52 

I9.92 

18.95 

82 

3-21 

3-51 

23 

44-03 

42-50 

53 

19.14 

18.21 

83 

2.92 

3.26 

24 

43-19 

41.72 

54 

18-35 

17.48 

84 

2.64 

3-ot 

25 

42.36 

40.89 

55 

I7-58 

16.76 

85 

2.36 

2-79 

26 

41-53 

40.06 

56 

16.82 

16.04 

86 

2.07 

2-57 

27 

40.69 

39-22 

57 

16.08 

15-35 

87 

1.81 

2-35 

28 

39-86 

38.39 

58 

15-34 

14.67 

88 

J-59 

2.12 

29 

39-02 

37-56 

59 

14.62 

14.00 

89 

1.38 

I.gi 

3° 

38.18 

36.73 

60 

*3-9l 

13-34 

90 

1.16 

1.72 

3i 

37-34 

35-90 

61 

13.22 

12.70 

91 

•94 

i-54 

32 

36-51 

35-07 

62 

12.55 

12.08 

92 

•79 

i-35 

33 

35-67 

34-24 

63 

11.69 

11.47 

93 

.69 

I-IS 

34- 

34-83 

33-41 

64 

11.25 

10.88 

94 

.58 

•97 

35 

33-99 

32.58 

65 

10.63 

10.31 

95 

•50 

•So 

36 

33-15 

31.76 

66 

10.03 

9-76 

96 

•77 

37 

32-31 

30.93 

67 

9.46 

9-23 

97 

.... 

•72 

38 

3i-47 

30.11 

68 

8.90 

8.71 

98 

.... 

•67 

1    39 

30.63 

29.29 

69 

8-37 

8.22 

99 



•50 

at  66.50  years  of  age  ;  and,  subtracting  the  age  of  the  person  from 
this  quantity,  we  have  66.50—20=46.50,  the  equation  of  life. 


OF  LIFE   INSURANCE.  59 

The  expectation  of  life  at  age  20  is  42.20  years,  and  would 
be  reached  at  age  62.20,  when  there  are  54,400  living,  or 
8,082  more  than  half  the  tabular  number  at  the  age  20. 

The  equation  of  life  may  be  found  by  the  following  rule : 
Take  half  the  tabular  number  living  at  the  given  age,  divide  the 
difference  between  this  quotient  and  the  tabular  number  of  the 
living  at  the  next  preceding  age  where  the  number  of  living  is 
greater  than  this  quotient,  by  the  number  of  dying  in  that  age 
where  the  equation  occurs,  the  result  is  the  fractional  part  of  the 
year  required.  The  integral  part  of  the  equation  may.  be  found 
by  subtracting  the  given  age  from  the  age  in  which  the  equation 
is  found,  as  in  the  preceding  example. 

JOINT-LIFE   POLICIES. 

Joint-life  policies,  as  issued  in  this  country,  are  made  payable 
to  the  survivor  on  the  death  of  one  of  two  lives,  both  parties 
being  insured  under  the  same  policy.  In  this  class  of  policies 
the  probability  that  either  one  of  two  persons  will  survive  a 
given  period  of  time  is  less  than  the  probability  that  each 
separate  life  will  continue  the  same  length  of  time.  It  is 
evident,  with  very  little  demonstration,  that  if  A  aged  60  and  B 
aged  70  were  insured  on  the  same  joint-life  policy  the  proba- 
bility that  one  of  the  two  will  die  within  a  year  is  greater 
than  the  probability  that  either  of  the  two  taken  separately 
will  die  during  that  time.  If  the  probability  that  A  will 

live  for  one  year  be  —  and  B's  probability  of  living  is  —  then 
the  probability  that  both  of  them  will  survive  this  period  is 

—  x  —  =  —  and  the  probability  of  one  of  the  two  dying  during 
10       10       100  * 

year  is  i  —  —  =  — -.     In  making  this  calculation  we  assume  that 

J  IOO  100 

A  has  only  —  of  a  certainty  of  living  one   year   and   B   only 

Q 

— ,  therefore  the  chance  of  both  living  would  be  in  A's  case  not 

—  of  a  year  but  —  of  B's  —  =  — ,  and  in  B's  case  the  chance 

10  10  10  100 

would  be  —  of  —  =  -?—-.  As  the  supposed  mortality  on  A's  single 


life  is  only  —  and  on  B's  —  the  risk  on  their  joint  lives  would 

J     IOO  IOO  •* 


60  PRINCIPLES  AND  PRACTICE 

be  much  greater  than  upon  either  life  taken  separately,  and  since 
the  premiums  on  policies  increase  with  the  probability  of  dying, 
though  not  exactly  in  the  same  ratio,  it  is  easy  to  see  from  this 
illustration  that  the  premiums  on  joint  life  policies  should  be 
considerably  larger  than  those  on  policies  for  single  lives. 

It  is  not  intended  in  this  place  to  enter  upon  a  full  explana- 
tion of  the  intricate  calculations  involved  in  the  computation  of 
joint  life  premium  rates,  but  we  propose  to  give  only  such  tables 
as  will  be  of  value  to  the  public.  As  a  general  rule,  joint-life 
policies  are  not  regarded  with  much  favor  by  American  compa 
nies.  Many  of  the  most  prominent  companies  have  refused  to 
issue  them  or  have  abandoned  them  after  a  few  years'  trial,  while 
other  companies  have  large  numbers  upon  their  books. 

Required  the  probability  that  two  lives  aged  25  and  35  will 
both  live  one  year.  The  probability  of  the  life  age  25  = 

89032  =  '991936-  The  probability  of  the  life  aged  35  =  |jg?  = 
.991054.  Multiplying,  .991936  x  991054  =  .983062.  The  prob- 
ability that  one  of  the  two  will  die  within  a  year  is  i  —  .983062 
=  .016938. 

THE  RETURN-PREMIUM  PLAN. 

By  •  this  plan  a  company  contracts  to  return  to  the  policy- 
holder  the  whole  amount  of  the  sum  insured  at  death  or  expira- 
tion of  the  policy  when  the  full  number  of  premiums  have  been 
paid,  and  also  to  return  the  whole  amount  of  premiums  without 
interest. 

We  assume  that  the  legitimate  object  of  life  insurance  is  to 
obtain  the  greatest  amount  of  insurance  at  the  least  cost,  that  is, 
to  throw  as  great  a  burden  as  possible  upon  the  company  with  a 
due  regard  to  the  length  of  the  time  in  which  the  payments  will 
be  made  and  exercising  a  reasonable  caution  against  making  the 
payments  too  heavy  in  the  unproductive  period  of  old  age. 

In  order  to  enable  the  company  to  afford  to  return  the  whole 
amount  of  premiums  paid  when  the  claim  is  due,  it  is  necessary 
to  charge  a  larger  annual  premium  during  the  continuance  of 
the  policy.  The  company  cannot  afford  to  return  all  the  pre- 
miums without  being  repaid  for  this  obligation  by  a  greater 
reserve,  a  greater  accumulation  of  interest,  and  a  less  amount  at 
risk  for  the  same  money  than  in  the  ordinary  nnethods  of  insu- 


OF  LIFE   INSURANCE. 


6l 


ranee.  It  is  plain  that  he  who  chooses  this  form  of  policy  seeks 
a  future  good  by  paying  a  greater  premium  and  obtaining  less 
insurance. 

As  an  illustration  of  the  workings  of  the    return-premium 
plan  we  take  the  columns  as  given  in  the  following  table : 

TABLE  No.  XII. 
RETURN  PREMIUMS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


A. 

B. 

c. 

D. 

E. 

A  re* 

Net  Annual  Pre- 
mium to  insure 
$  i  .000  for  whole 

Amount  of  Insur- 
ance for  the  first 

Amount  of  Insurance 
on    the    ordinary 
•whole  life  plan  pur- 
chased by  a  net  an- 

No. of 
Premiums 

•Age. 

lift;,  premiums 
returned     at 
death,   -without 

year  on  the  Re- 
turn-Pretn  turn 
Plan. 

nual  premium  equal 
to   that  charged   in 
the  Return-Premium 

to  be  paid 
before  C=D 

interest. 

plan  at  the  same  age. 

IO 

$I3-584 

$1013.584 

$1362.078 

27 

15 

I5-247 

1015.247 

1406.161 

27 

2O 

17.472 

1017.472 

1460.137 

27 

25 

20.496 

1020.496 

1526.931 

26 

30 

24.687 

1024.687 

1609.742 

25 

35 

30.630 

1030.630 

I7I3-375 

24 

40 

39.284 

1039.284 

I844-233 

22 

45 

52.261 

1052.261 

2OII.I2I 

2O 

5° 

72-3*3 

1072.313 

2225.700 

17 

55 

103.986 

1103.986 

2504.058 

15 

60 

I55-365 

"55-365 

2869.637 

13 

65 

241-331 

1241.331 

3356.575 

IO 

70 

389-633 

I389-633 

4017.001 

8 

Column  A  gives  the  age  of  the  policyholder  ;  B,  the  net  annual 
premium  on  the  return-premium  plan  ;  C,  the  amount  of  insur- 
ance the  first  year  on  this  plan  ;  D,  the  amount  of  insurance  which 
could  be  purchased  by  the  premiums  in  column  B  if  the  party 
were  insured  on  the  whole-life  plan ;  and  E,  the  number  of  pre- 
miums necessary  to  be  paid  in  order  that  column  C  may  equal 
D.  At  age  30  the  net  annual  return  premium  is  $24.687 
which  secures  for  the  first  year  $1024.687  insurance,  but 
insured  on  the  whole-life  plan  with  the  same  amount  of  premium 
the  policyholder  would  get  $1609.742  insurance  and  the  policy- 
holder  insured  by  the  first  method  has  to  make  25  payments  be- 
fore his  policy  increases  to  $1609.742,  the  amount  to  be  obtained 
on  the  whole-life  plan.  At  age  55  the  policyholder  in  the 
return-premium  plan  pays  an  annual  premium  $103.986  and 
obtains  the  first  year  $1103.986  insurance  but  on  the  whole-life 
plan  he  could  have  $2504.058  or  $1400.072  more  insurance  the 


62 

first  year  and  not  till  he  has  made  15  payments  or  till  he  has 
reached  the  age  of  69  will  his  policy  be  larger  than  if  he  had 
adopted  the  whole  life  plan. 

FORFEITURE   OF    POLICIES  AND  PAID-UP    INSUR- 
ANCE. 

A  policy  of  life  insurance  is  a  contract  whereby  the  company, 
for  a  certain  consideration,  agrees  to  indemnify  the  policyholder, 
his  heirs  or  assigns,  in  case  of  his  death  or  at  a  certain  period  if 
living,  according  to  the  terms  expressed  therein.  One  part  of 
the  contract  is  that  the  premiums  shall  be  regulai'ly  paid  during 
the  time  specified.  The  company  cannot  violate  this  contract, 
until  the  policy  becomes  payable,  except  by  refusing  to  receive 
the  premiums  and  keep  the  policy  in  force  upon  the  books.  But 
it  is  comparatively  easy  and  a  frequent  practice  for  the  policy- 
holder  to  violate  his  part  of  the  contract  and  to  refuse  or  neglect 
to  pay  the  premiums  due.  In  the  meantime,  the  company  holds 
an  unearned  deposit  or  reserve,  to  accumulate  and  meet  the 
future  claim.  The  neglect  to  pay  the  premium  constitutes  the 
first  violation  of  the  contract,  and  the  policyholder  cannot  legally 
claim  any  favors  from  the  company  after  this.  But  there  may  be 
a  moral  injustice  done  to  the  policyholder  in  refusing  to  make 
any  compromise  with  him.  Since  he  has  paid  money  for  insur- 
ance which  he  has  not  got,  it  is  but  just  that  he  should  have  all 
the  company  can  afford  to  restore. 

With  a  limited  payment  life  or  endowment  policy,  the  rule 
usually  adopted  is  to  issue  a  paid-up  policy  for  such  a  fractional 
part  of  the  sum  insured  as  the  number  of  payments  made  bears 
to  the  whole  number  promised.  But  in  the  case  of  a  continued 
premium  life  policy,  the  case  is  different.  In  this  form  of  insur- 
ance, there  is  the  least  for  the  policyholder  to  sacrifice,  and  there- 
fore the  temptation  to  allow  the  policy  to  lapse  is  often  very 
strong.  Although  the  policyholder,  by  violating  the  conditions, 
has  forfeited  all  claim  upon  the  company  unless  otherwise 
agreed  upon,  yet  public  opinion  naturally  frowns  upon  a  company 
which  absorbs  the  unearned  premiums  for  the  benefit  of  other 
policyholders.  Beyond  protecting  itself  from  loss,  the  company 
should  derive  no  undue  advantage  from  the  inability  of  a  policy- 
hoMer  to  pay  the  annual  premium.  It  is  this  which  has  made 


OF  LIFE  INSURANCE.  63 

the  non-forfeiture  law  of  Massachusetts  and  the  non-forfeiture 
regulations  of  some  companies  of  other  states,  a  means  of  remov- 
ing, to  some  extent,  one  of  the  harsh  features  of  life  insurance. 
In  life  insurance  more  than  in  almost  any  other  business,  the 
public  need  the  'most  perfect  confidence,  not  only  that  the  legal 
obligations  of  the  companies  will  be  fulfilled,  but  that  they  or 
their  legal  representatives  will  be  equitably  dealt  by,  and  this 
has  become  one  of  the  first  conditions  to  the  prosperity  of  the 
business. 

The  forfeiture  of  policies  for  the  non-payment  of  premiums 
was  quite  common  ten  years  ago,  when  the  whole-life  plan  of 
insurance  was  the  one  usually  adopted,  and  the  sacrifices  which 
policyholders  were  sometimes  compelled  to  make,  in  losing  not 
only  the  whole  of  the  reserves,  but  reversionary  paid-up  insurance, 
was  a  hardship  which  loudly  demanded  a  reform.  In  the  year 
1859,  the  subject  was  first  brought  before  the  legislature  of  Mas- 
sachusetts by  Hon.  Elizur  Wright,  the  insurance  commissioner, 
which  resulted,  in  1861,  in  the  passage  of  the  non-forfeiture  law 
of  that  state. 

In  England  also,  previous  to  this  time,  non-forfeiture  policies 
had  been  strenuously  advocated  by  Dr.  Farr.  It  is  highly 
probable  that  this  eminent  actuary  was  the  first  to  propose  and 
advocate  the  payment  of  a  definite  cash  surrender  value  to  a 
policy.  Many  years  ago  he  demonstrated  what  was  the  portion 
of  yearly  premium  which  was  necessary  to  secure  the  company 
against  loss  and  what  might  be  withdrawn  by  the  policyholder 
in -anticipation  of  his  future  claim.  The  plans  of  Dr.  Farr  were 
adopted  by  the  British  Imperial  Life  Association,  where  any 
policyholder  has  a  right  to  withdraw  from  the  company  a  definite 
proportion  of  the  premiums  he  has  paid.  The  Massachusetts 
non-forfeiture  law,  above  alluded  to,  compels  the  company,  in 
case  the  policyholder  neglects  to  pay  the  premiums,  to  continue 
the  policy  in  force  as  a  paid-up  policy  of  temporary  insurance  so 
long  as  four-fifths  of  the  cash  reserve  computed  according  to  the 
Actuaries'  Table  of  mortality  and  4  per  cent  interest  would  sus- 
tain it. 

This  law  was  intended  to  apply  exclusively  to  whole  life  poli- 
cies. At  the  time  when  the  law  was  proposed  in  1859,  there  were 
very  few  endowment  or  limited-term  life  policies  in  force  in  the 


64 


PRINCIPLES  AND  PRACTICE 


companies  doing  business  in  Massachusetts — the  policies  issued 
up  to  that  time  having  been  almost  entirely  confined  to  the  whole- 
life  plan.  The  clause  in  the  law  which  allows  the  companies  to 
deduct  from  the  amount  insured,  when  the  policy  became  a  claim, 
the  unpaid  premiums  and  interest  thereon  at  6  per  cent  interest, 
weakens  its  force  to  a  great  extent  when  applied  to  short  term 
endowments  and  life  policies  with  a  limited  number  of  pay- 
ments. 

This  peculiarity  of  the  law  is  easily  shown  by  taking  the 
example  of  a  fifteen-payment  endowment  for  $1,000,  issued  at 
age  40,  payable  at  death  or  55,  annual  premium  $69.49.  Sup- 
pose that  after  five  annual  payments  have  been  made,  the 
payment  of  premiums  is  discontinued,  and  then,  according  to  the 
operation  of  this  law,  a  term  policy  for  twenty-two  years  is 
allowed.  At  the  end  of  the  fifteen  years  from  the  date  of  the 
policy,  or  ten  years  after  the  payment  of  premiums  ceased,  the 
policyholder,  in  the  event  of  death,  would  leave  to  his  heirs 
only  the  amount  of  $1,000  less  the  unpaid  premiums  and  interest, 
or  $1,000  —  $970.89  =  $29.11,  and  the  greater  (he  loading  on  the 
premiums  the  less  the  insurance  which  is  obtained.  That  is,  the 
amount  insured  constantly  decreases,  and  decreases  faster  under 
mutual  than  under  non-participating  rates.  In  another  part  of 
this  work  we  give  some  tables  for  the  calculation  of  insurance 
due  on  lapsed  policies,  according  to  this  law. 

SURRENDER  VALUES. 

No  subject  in  life  insurance  is  more  thoroughly  discussed  at 
the  present  day  than  the  proper  rule  for  determining  the  surrender 
value  of  a  policy.  The  common  method  of  computing  the  sur- 
render value  is  to  deduct  from  the  reserve  25  to  50  per  cent,  as  a 
surrender  charge,  and  pay  the  remainder  as  an  equitable  sur- 
render value.  But  this  method  is  held  to  be  wrong  in  principle, 
for  the  longer  a  policyholder  remains  in  a  company,  and  conse- 
quently the  less  benefit  he  can  confer  upon  it  by  the  payment  of 
his  annual  premium,  the  greater  will  be  his  surrender  charge. 
In  other  words,  the  longer  he  stays  in  the  company  the  more  it 
will  cost  him  to  get  out. 

Every  policyholder  when  he  comes  into  a  company  is  expected 


OF  LIFE   INSURANCE.  65 

to  confer  a  benefit  upon  it  by  his  annual  contributions  ;  and,  if  he 
leaves  the  company  by  allowing  his  policy  to  lapse,  he  inflicts 
an  injury  upon  it  equal  to  the  present  value  of  the  future  profit 
which  the  company  would  receive  from  the  transaction.  What 
is  the  measure  of  this  injury,  or  what  basis  shall  we  adopt  for 
ascertaining  it?  Mr.  Wright  says  that  the  present  value  of  the 
future  cost  of  insurance,  which  he  calls  "  insurance  value,"  should 
be  the  basis,  and  that  the  surrender  charge  should  be  a  percent- 
age on  this  insurance  value.  Prof.  Bartlett,  Actuary  of  the 
Mutual  Life,  of  New  York,  takes  similar  ground,  when  he 
says  that  "the  company's  interest  in  any  particular  policy  is  the 
present  value  of  the  sums  the  policy  would,  if  continued  in  the 
company  in  its  present  condition,  contribute  from  year  to  year 
to  pay  death  claims  on  other  policies."  Upon  this  basis  some 
very  ingenious  formulae  for  computing  surrender  values  have 
been  made.  This  theory  of  "insurance  value"  may  be  correct 
so  far  as  the  policyholder  is  concerned,  but  it  fails  to  do  justice 
to  the  companies.  The  "  cost  of  insurance,"  as  regards  the 
companies,  is,  in  addition  to  the  policyholder's  contribution  to 
losses,  as  given  in  the  cost-of-insurance  tables,  all  his  propor- 
tion of  office  expenses,  salaries,  license  fees,  etc., — everything  re- 
quired to  sustain  the  company  as  an  efficient  working  organiza- 
tion. When  the  company  receives  an  application  for  a  policy  of 
insurance,  it  receives  also  a  virtual  pledge  that  the  applicant  will 
make  his  annual  contributions  to  the  support  of  the  company  as 
a  corporation,  besides  what  is  necessary  to  pay  death  claims  and 
endowments.  This  view  of  the  subject  seems  the  more  reason- 
able, because  under  this  new  rule  the  company  is  supposed  to 
cut  off  all  profits  from  lapsed  policies  as  a  source  of  income,  and 
make  only  such  a  surrender  charge  as  will  prevent  the  company 
from  incurring  any  loss.  Now  these  two  things  are  perfectly 
clear,  the  policyholder  has  agreed  to  make  certain  contributions 
towards  the  future  losses  of  the  company  and  the  running  ex- 
penses, and  by  paying  a  percentage  on  the  insurance  value  he 
has  recompensed  the  company  for  only  one  of  them.  A  surrender 
charge,  made  by  taking  a  percentage  of  the  present  value  of  the 
unexpired  gross  premiums  from  the  reserve,  has  been  proposed 
as  a  method  of  finding  an  equitable  surrender  value  for  all  kinds 
of  policies.  Some  of  the  advantages  of  this  method  are  that  it 
gives  a  better  practical  adjustment  of  the  surrender  charges  on 


66  PRINCIPLES  AND  PRACTICE 

whole-life  and  short-term  endowment  policies,  than  by  taking  a 
percentage  on  the  insurance  value,  and  that  the  surrender  charge 
each  subsequent  year  is  less  than  the  one  preceding. 

AVERAGE  DURATION  OF  POLICIES. 

This  is  a  subject  which  has  always  been  ignored  in  life  insur- 
ance calculations,  since  all  policies  are  issued  upon  the  assump- 
tion that  the  future  premiums  are  to  be  promptly  paid,  while  in 
practice  the  average  duration  of  policies  is  much  less  than  the 
tabular  duration.  In  every  company  a  large  number  of  policies 
Ip.pse  after  a  few  payments,  but  as  most  companies  give  either  a 
surrender  value  on  being  released  from  the  contract,  or  a  paid-up 
policy  for  a  fractional  part  of  the  sum  insured,  this  result  makes 
but  little  change  in  the  ratio  of  liabilities  and  assets.  But  cases 
sometimes  arise  when  agents  wish  to  know  the  present  value  of 
their  future  commissions,  and  then  the  future  duration  of  the 
policies  must  be  estimated.  Unfortunately  no  statistics  on  this 
subject  derived  from  the  experience  of  American  companies 
have  been  published. 

The  combined  statistics  returned  by  fifteen  life  offices  in 
England  show  that  the  average  lifetime  of  a  policy  in  these 
companies,  up  to  the  year  1843,  was  less  than  five  and-a-half 
years ;  in  the  Gotha  Life,  of  Germany,  it  was  a  little  over  eight 
years;  and  in  the  Equitable  Life,  of  London,  twelve  and-a-half 
years.  In  the  seventeen  life  offices  the  average  duration  of  life, 
after  insuring,  of  the  policyholders  who  died  was  6.413  years. 

In  the  Massachusetts  Report  for  1861,  we  find  that  on  2,180 
policies  which  had  been  forfeited  in  companies  doing  business 
in  that  state,  7-646  premiums  had  been  paid,  making  the  average 
duration  of  each  lapsed  policy  3.51  years. 


68 


PRINCIPLES  AND   PRACTICE 


TABLE   XIII. 
AMERICAN  EXPERIENCE  MORTALITY  TABLE. 


Age. 

Number  survi- 
ving at  each  age. 

Deaths  in  each 
year. 

Age. 

Number  survi- 
ving at  each  age. 

Deaths  in  each 
year. 

10 

100,000 

749 

55 

64,563 

>r99 

II 

99.251 

746 

56 

63,364 

,260 

12 

98'5°5 

743 

57 

62,104 

.325 

13 

97,762 

740 

58 

60,779 

,394 

H 

97,022 

737 

59 

59'385 

,468 

15 

96,285 

735 

60 

57,9*7 

,546 

16 

95-550 

732 

61 

56,37i 

1,628 

i7 

94,818 

729 

62 

54,743 

L7I3 

18 

94-089 

727 

63 

53-030 

i,  800 

*9 

93^62 

725 

64 

5I,23° 

1,889 

20 

92>637 

723 

65 

49,341 

1,980 

21 

91,914 

722 

66 

47,36i 

2,070 

22 

91,192 

721 

67 

45,291 

2,158 

23 

90,471 

720 

68 

43,133 

2,243 

24 

89.751 

719 

69 

40,890 

2,321 

25 

89,032 

718 

70 

38,569 

2.391 

26 

88.314 

718 

71 

36,178 

2,448 

27 

87.596 

718 

72 

33,730 

2,487 

28 

86,878 

718 

73 

3L243 

2,505 

29 

86,160 

719 

74 

28,738 

2,501 

30 

85.441 

720 

75 

26,237 

2,476 

3i 

84,721 

721 

76 

23,761 

2,43i 

32 

84.000 

723 

77 

21,330 

2,369 

33 

83.277 

726 

78 

18,961 

2.261 

34 

82,551 

729 

79 

16,670 

2,196 

35 

81.822 

732 

So 

H,474 

2.091 

36 

81,090 

737 

Si 

12,383 

1,964 

37 

8o.353 

742 

82 

10,419 

1,816 

38 

79.611 

749 

83 

8,603 

1,648 

39 

78.862 

756 

84 

6,955 

1,470 

40 

78,106 

765 

85 

5,485 

1,292 

4i 

77.341 

774 

86 

4,193 

1,114 

42 

76,567 

785 

87 

3,079 

933 

43 

75-782 

797 

88 

2,146 

744 

44 

74-985 

812 

89 

1,402 

555 

45 

74,173 

828 

90 

847 

385 

46 

73-345 

848 

91 

462 

246 

47 

72.497 

870 

92 

216 

137 

48 

71,627 

896 

93 

79 

58 

49 

70-731 

927 

94 

21 

18 

50 

69.804 

962 

95 

3 

3 

ri 

68,842 

I,OOI 

06 

O1 
C2 

67.841 

I  O<1A 

yu 

O7 

3* 

C7 

\j  /  '^"r* 
66.7Q7 

•*'(-"TT 

I  OOI 

y/ 
oS 

JO 
C  A 

wv>.  fyi 

6c  706 

i,^_/y  i 
T    147 

y° 

no 

64 

J,  /*-"-' 

i.*4j 

99 

OF  LIFE  INSURANCE, 


69 


TABLE   No.  XIV. 
COMBINED  EXPERIENCE  MORTALITY    TABLE. 


Age. 

Number  survi- 
ving at  fetch  age. 

Deaths  in  each 
year. 

Age. 

Number  survi- 
ving at  each  age. 

Deaths  in  each 
year. 

10 

100,000 

676 

55 

63,469 

L375 

ii 

99,324 

674 

56 

62,094 

L436 

12 

98,650 

672 

57 

60,658 

L497 

'3 

97,978 

671 

58 

59>l6i 

1,561 

M 

97.307 

67I 

59 

57,600 

1,627 

15 

96,636 

67I 

60 

55.973 

1,698 

16 

95.965 

672 

61 

54,275 

1,770 

IT 

95.293 

673 

62 

52,505 

1,844 

IS 

94,620 

675 

63 

50,661 

i,9i7 

19 

93.945 

677 

64 

48,744 

1,990 

20 

93.268 

680 

65 

46,754 

2,061 

21 

92,588 

683 

66 

44.693 

2,128 

22 

9I'9°5 

686 

67 

42,565 

2,191 

23 

91,219 

690 

68 

40,374 

2,246 

24 

90,529 

694 

69 

38,128 

2,291 

^5 

89.835 

698 

70 

35,837 

2,327 

26 

89-I37 

703 

7i 

33,5!0 

2,35i 

27 

88-434 

708 

72 

3i,i59 

2,362 

28 

87,726 

7'4 

73 

28,797 

2,358 

29 

87,012 

720 

74 

26,439 

2,339 

30 

86.292 

727 

75 

24,100 

2,303 

3i 

85,565 

734 

76 

21,797 

2,249 

32 

84,831 

742 

77 

*9.548 

2,179 

33 

84,089 

750 

78 

17-369 

2,092 

34 

83-339 

758 

79 

15,277 

1,987 

35 

82,581 

767 

80 

13,290 

1,866 

36 

81,814 

776 

81 

11,424 

i,73o 

37" 

81,038 

785 

82 

9,694 

1,582 

38 

80,253 

795 

83 

8,112 

1,427 

39 

79.458 

805 

84 

6,685 

1,268 

40 

78,653 

815 

85 

5,417 

1,111 

4i 

77.838 

826 

86 

4,306 

_  _o 

95" 

42 

77,012 

839 

87 

3,348 

811 

43 

76,i73 

857 

88 

2,537 

673 

44 

75.3i6 

881 

89 

1,864 

545 

45 

74.435 

909 

90 

i,3i9 

427 

46 

73.526 

944 

9i 

892 

322 

47 

72,582 

981 

92 

57° 

231 

48 

71,601 

1,021 

93 

339 

155 

49 

70,580 

.063 

94 

184 

95 

50 

69.517 

,108 

95 

89 

52 

5i 

68,409 

,156 

96 

37 

24 

52 

67.253 

,207 

97 

13 

9 

53 

66,046 

,261 

98 

4 

3 

54 

64,785 

>3l6 

99 

i 

i 

PRINCIPLES  AND  PRACTICE 


TABLE  No.   XV. 
COMMUTATION  COLUMNS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


4 

Dx. 

NX. 

Cx. 

MX. 

JR*. 

IO 

64,392-77 

1,214,144.09 

461.5329 

12,109.051 

322.708.03 

II 

61,158.34 

1,149,751.32 

439.8893 

11,647-519 

310,59898 

12 

58,084.84 

1,088,592.98 

419.2538 

11,207.6:9 

298,951  46 

13 

55,164.32 

1,030.508.14 

399-5799 

10,788.375 

287.743.83 

52,389.25 

975.343-82 

380.8230 

10,388.796 

276-955-46 

15 

49,752-44 

922,954.57 

363-4350 

10,007.973 

266,566.66 

16 

*  873,202.  15 

346-3651 

9,644.538 

256,558.69 

17 

.  .  O/"  GSR^C* 

4^pO53PrV 

825,955.60 

330-0915 

9,298.173 

246.914.15 

18  , 

•4jap-53 

781,089.96 

315.0104 

8,968.081 

237,615.98 

19 

V4&.453-93 

738,486.43 

300.6161 

8,653.071 

228,647.90 

20 

38,411.27 

698,032.51 

286.8773 

8,352-455 

219.994.83 

21 

36,470.32 

659,621.24 

274.1440 

8,065.577 

211,642.37 

22 

34,625.68 

623,150.92 

261.9754 

7,79i-433 

203,576.79 

23 

32,872.65 

588,525-23 

250-3465 

7,529-458 

195,785-36 

24 

31,206.73 

555,652.58 

239-2333 

7,279.111 

188,255.90 

25 

29,623.67 

524,445-85 

228.6130 

7,039.878 

180.976.79 

26 

28,119.40 

494,822.18 

218.7684 

6,811.265 

173-936-91 

27 

26,689.75 

466,702.78 

209.3478 

6,592-497 

167,125.65 

28 

25,331.08 

440.013.04 

200.3328 

6,383-  H9 

160,533.15 

29 

24.039-93 

414,681.96 

191.9730 

6,182.816 

154,150.00  j 

30 

22,812.75 

390.642.02 

183.9617 

5,990.843 

147,967.19 

31 

21,646.42 

367,829.28 

176.2844 

5,806.881 

141.976.34 

32 

20,537-99 

346,182.86 

169.1612 

5,630.597 

136.169.46 

33 

19,484.42 

325,644.86 

162.5484 

5.461.436 

130,538.87 

34 

18,482.83 

306,160.44 

156.1915 

5,298.887 

125-077-43 

35 

17.530.73 

287,677.61 

150.0806 

5,142.696 

119.778.54 

36 

16,625.73 

270,146.89 

144.5988 

4,992.615 

114.635.85 

37 

15,765.20 

253,521.15 

139.3108 

4,848.016 

109.643.23 

38 

14,947.00 

237.755.96 

134-5695 

4,708.706 

104.795.22 

39 

14,168.78 

222,808.96 

129.9781 

4,574-i36 

100,0^6.51 

40 

13,428.66 

208,640.18 

125.8617 

4,444.158 

95-5I2-375 

12,724-53 

195,211.51 

121.8588 

4,318.296 

91.068.217 

42 

12,054.73 

182,486.08 

118.2685 

4,196.438 

86.749-920 

43 

11,417.36 

170.432.25 

114.9057 

4,078.169 

82.553-483 

44 

10,810.79 

159,014.90 

112.0271 

3,963.263 

7S,475-3I4 

45 

10,233.23 

148.204.10 

109-3153 

3,851.236 

74.512.050 

46 

9,683.250 

137.970.87 

107.1347 

3,741.921 

70.660.814 

47 

9,  '59-  '33 

128,287.62 

105.1810 

3,634-786 

66.918.893 

48 

8,659.540 

119,128.49 

103-6597 

3,529.605 

63,284.107 

49 

8,182.981 

110,468.95 

102.6278 

3,425.946 

59-754-502 

50 

7,727.976 

102,285.96 

101.9164 

3-323-318 

56.328.556 

7,293.276 

94-557-9S9 

101.4815 

3,  221.401 

53.005.239 

52 

6,877.730 

87.264.712 

101.2831 

3.119.920 

49-7S3-\17 

53 

6,480.277 

80,386.982 

101.2850 

3,018.637 

46.663.918 

54 

6,099.937 

73,906.705 

101.5431 

2,917.352 

43,645.281 

OF  LIFE  INSURANCE. 


TABLE  No.  XV— (CONTINUED.) 
COMMUTATION  COLUMNS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


4 

Dx. 

Nx. 

c*. 

Mx. 

Rx. 

55 

5.735-71? 

67,806.768 

101.9312 

2,815.809 

40,727.929 

56' 

5,386.794 

62,071.052 

102.5043 

2,7i3-877 

37,912.121 

57 

^052.322 

56,684.258 

103.1504 

2,611.373  ' 

35,198.243 

58 

4.731-607 

Si,  63  1.  936 

103.8488 

2,508.223 

32,586.8/0 

59 

4,424.005 

46,900.329 

104.6523 

2,404-374 

30.078.647 

60 

4.128.846 

42,476.324 

105.4668 

2,299.722  . 

27,674.274 

61 

3,845-582 

38,347-478 

106.2782 

2,i94-255-.  .  ' 

^5-374-552 

62 

3  073-704 

34,501.897 

107.0117 

2,087.977 

23  ,'1=80.297 

63  3.312.801 

30,928.193 

107.6044 

1,980.965 

3-1,092.  320 

64  3,062.540 

27,615.392 

108.0620 

1,873-361 

19,111.356 

65  2,822.598 

24>552-85i 

108.3902 

1,765.299 

17,237-995 

66  2,592.661 

21,730-253 

108.4373 

1,656.908 

15.472.697 

.67  2.372.578 

19,  137-592 

108.1792 

1,548.471 

13,815-788 

68 

2,  -62.  230 

16,765.014 

107-5983 

1,440.292 

12.267.317 

69 

1,961.522 

14,602.784 

106.5454 

1.332.694 

10,827.025 

70 

1,770-509 

12,641.263 

105.0323 

1,226.148 

9,494-3319 

7i 

1,589.234 

10,870.754 

102.9055 

1,  121.116 

8,268.1839 

72 

i»4I7-893 

9.281.520 

100.0430 

1,018.210 

7,147.0681 

73 

1.256.792 

7.863.627 

96.42778 

918.1673 

6,128.8578 

74 

1,106.244 

6,606.834 

92.12806 

821.7395 

5,210.6905 

75 

966.4790 

5.500.590 

87-27957 

729.6114 

4.388.9510 

76 

837.5807 

4,534-m 

82.00317 

642.3319 

3,659-3395 

77 

7  i  9-  5095 

3,696.530 

76.47059 

560.3287 

3,017.0077 

78 

612.0552 

2,977.021 

70.76821 

483.8581 

2.456.6789 

79 

514.9306 

2,364.966 

64.91260 

413.0899 

1,972.8208 

80 

427.8438 

1,850.035 

59.14724 

348.1773 

i'559-73°9 

Si 

350-2727 

1,422.191 

53-16253 

289.0301 

1,211.5536 

82 

282.0267 

1,071.9185 

47.03961 

235-S675 

922-52352 

33 

222.8424 

789.89177 

40.84970 

188.8279 

6S6.6s  =598 

84 

172.3966 

567.04938 

34.86844 

147.9782 

497.82805 

85 

130.1044 

394.65274 

29-3-659 

1  13.-!  098 

349.84982 

86 

95-I7523 

264-54837 

24.19736 

83-783I9 

236.74004 

S7 

66.87942 

l69-373H 

19-39314 

59-5S5S3 

152.95684 

8S 

44.60631 

102.49372 

14.79868 

40.19269 

93-37IOH 

89 

27.88676 

57.88742 

10.56396 

25-3940I 

53.178320 

90 

16.12194 

30.00064 

7.012586 

14.83005 

27.784310 

91 

8.415*04 

13-87871 

4.287819 

7.8174590 

12.954265 

92 

3-  76491  5 

5.463611 

2.285102 

3.5296396 

5.  1  368;  .62 

93 

1.317687 

1.698697 

.9257566 

'•2445372 

1.6071665 

94 

0.335  iss 

0.381009 

.2749318 

.3187806 

.36262938 

95 

0.045822 

0.045822 

.0438488 

.0438488 

.04384878 

PRINCIPLES  AND  PRACTICE 


TABLE  NO.  XVI. 
COMMUTATION  COLUMNS,  COMBINED  EXPERIENCE,  4  PER  CENT- 


Age. 

Dx. 

Nx.  ' 

cx. 

M». 

10 

67*556.41 

1,381,771.74 

439.1167 

14.411.3725 

II 

64,519.00 

1,314,215.33 

420.9784 

x3,972-2557 

12 

61,616.50 

1.249,696.33 

403-5858 

I3>55I-2772 

J3 

58,843.07 

1,188,079.83 

387.4858 

13,147.6913 

H 

56,192.36 

1,129,236.76 

372-5825 

12,760.2055 

IS 

53,658-54 

1,073.044.40 

358.2524 

12,387.6229 

16 

51,236.51 

1,019,385.86 

344.9868 

12,029.3704 

*7 

48.920.90 

968,149.35 

332.2118 

11,684.3835 

18 

46.707.10 

919,228.45 

320.3837 

11.352.1716 

19 

44.590-3o 

872,521.35 

308.9740 

11,031.7878 

20 

42,566.31 

827,931.05 

298.4068 

10,722.8137 

21 

40,630.73 

785.364-74 

288.1955 

10,424.4069 

22 

38.779-81 

744,734-01 

278.3283 

10,136.2113 

23 

37.009.94 

705,954.20 

269.1839 

9,857.8830 

24 

35.3i7-3i 

668.944.26 

260.3311 

9,588.6992 

25 

33-698.63 

633,626.95 

251.7611 

9,328.3681 

26 

32,15076 

599,928.32 

243.8120 

9,076.6069 

27 

30,670.39 

567-777-56 

236.1021 

8  832.7948 

28 

29,254.65 

537,107.17 

228.9451 

8.596.6926 

29 

27,900.53 

507,852.52 

221.9894 

8,367-7475 

30 

26,605.44 

479.951-99 

215.5266 

8,145.7580 

31 

25.366.64 

453.346-55 

209.2325 

7,930.2313 

32 

24,181.76 

427,979.91 

203.3779 

7,720.9987 

33 

23,048.32 

403,798.15 

197.6641 

7,517.6207 

34 

21,964.18 

380,749.83 

192.0889 

7,3i9-9565 

35 

20.927.31 

358,785-65 

186.8939 

7,127.8675 

36 

I9-935-52 

337,858.34 

181.8143 

6,940.9735 

37 

98.986.96 

317,922.82 

176.8491 

6,759-  J59* 

3S 

18,079.84 

298.935.86 

172.2134 

6,582.3100 

39 

17,212.25 

280,856.02 

167.6727 

6,410.0966 

40 

16,382.57 

263,643-77 

163.2265 

6,242.4238 

41 

15.589-24 

247,261.20 

159.0669 

6,079.1972 

42 

14.830.58 

231,671.96 

155-3561 

5,920.1302 

43 

14,104.82 

216,841.38 

152-5857 

5,764-7740 

44 

13,40974 

202,73606 

150.8258 

5,612.1882 

45 

12,743.16 

189.326.82 

149-6357 

5,461.3623 

46 

12,103.41 

176,583.66 

149.4188 

5,311.7282 

47 

11,488.47 

164,480.25 

149.3031 

5,162.3094 

48 

10,897.30 

152,991.78 

149.4143 

5,013.0062 

49 

10,318.76 

112,094.48 

149-5775 

4,863.5918 

50 

9,781.92 

131.765-72 

149.9131 

4,714.0142 

5i 

9-255-78 

121,983.80 

150.3918 

4,564.1010 

S2 

8.749.40 

112,728.02 

150-9873 

4.413.7091 

53 

8,261.90 

103,978.62 

i5I-6753 

4,262.7218 

54 

7,792.46 

95,716.72 

152.2026 

4,111.0465 

OF  LIFE  INSURANCE. 


TABLE  No.  XVI.—  (CONTINUED.) 
COMMUTATION  COLUMNS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

Dx. 

N*. 

a. 

Mx. 

55 

7-340-55 

87,924.26 

152.9100 

3,958.8437 

56 

6,905.30 

80,583.71 

153-5515 

3,805.9337 

57 

6,486.17 

73,678.41 

I53-9H75 

3,652.3821 

58 

6,082.78 

67,192.24 

I54-3249 

3,498.4644 

59 

5>694-5° 

61,109.46 

154-6633 

3>344-i394 

60 

5,320.82 

55,414.96 

155.2044 

3,189.4760 

61 

4,960.97 

50,094.14 

155-5630 

3,034.2715 

62 

4,614.60 

45^33-i7 

I55-8334 

2,878.7084 

63 

4,281.28 

40,518.57 

I55-77I7 

2,722.8749 

64 

3,960.85 

36,237.29 

155-4841 

2,567.1031 

65 

3.653-02 

32,276.44 

154.8380 

2,411.6189 

66 

3,357-68 

28.623.42 

I53-7227 

2,256.7808 

67 

3,074.82 

25,265.74 

152.1862 

2,103.0580 

68 

2,804.37 

22,190.92 

150.0063 

1,950.8717 

69 

2,546.50 

19,386.55 

147.1266 

1,800.8653 

70 

2,301-43 

16.840.05 

143.6909 

1,653-7385 

7i 

2.069.22 

14,538.62 

I39-5893 

1,510.0474 

72 

1,850.05 

12,469.40 

134.8485 

1,370.4580 

73 

1,644.05 

10,619.35 

129.4424 

1,235.6094 

74 

i,45i-37 

8,975.298 

123.4610 

1,106.1668 

75 

1,272.087 

7,523.928 

116.8853 

982.7057 

76 

1,106.275 

6,251.841 

109.7545 

865.8203 

77 

953-972 

5,145.566 

102.2484 

756.0657 

78 

815-0323 

4,i9J-594 

94.3904 

653.8171 

79 

689.2945 

3,376.5616 

86.2047 

559.4266 

80 

576.5783 

2,687.2671 

77.8415 

473.2219 

81 

476.5607 

2,110.6888 

69-3925 

395-3803 

82 

388.8389 

1,634.1281 

61.0154 

325.9878 

83 

312.8680 

1,245.2892 

52.9205 

264.9724 

84 

247.9142 

932.4212 

45-2153 

2i2.o=;i9 

85 

193-1637 

684.5070 

38.0931 

166.8365 

86 

147.6411 

491-3433 

31-5838 

128.7433 

87 

110.3786 

343.7022 

25.7091 

97-1594 

88 

80.4243 

233-3236 

20.5139 

7I-4503 

89 

56.81712 

152.8993 

15-9734 

50-9363 

90 

38-65848 

96.08221 

12.0336 

34-9630 

9i 

25-13852 

57-42373 

8.7255 

22.9294 

92 

I5-44572 

32.28521 

6.0188 

14.2039 

93 

8.83283 

16.83949 

3-8833 

8.1851 

94 

4.60983 

8.00665$ 

2.2885 

4.3018 

95 

2.14399 

3-396825 

1.2045 

2.0133 

96 

.85704 

1-252835 

•5345 

.8088 

97 

.28954 

•395795 

.1927 

•2743 

98 

.085663 

.106255 

.0618 

.0816 

99 

.020592 

.020592 

.0198 

.0198 

1 

74 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XVII. 
COMMUTATION  TABLES,  AMERICAN  EXPERIENCE,  6  PER  CENT. 


Age. 

Dx. 

NX. 

Cx. 

MX. 

Rx. 

10 

55-839-47 

853.966.39 

394-5637 

7,501.7416 

155.968.97 

ii 

52,284.18 

798,126.92 

370.7391 

7,107.1779 

148,467.23 

12 

48.953-97 

745.842.74 

348-3474 

6,736.4388 

141,360.05 

13 

45:834-65 

696.888.77 

327.3027 

6,388.0914;  134,623.61 

H 

42,912.92 

651.054.12 

307-5243 

6,060.7887    128,235.52 

15 

40,176.36 

608.141.20 

289.3300 

5,753-2644    122,174.73 

16 

37,612.90 

567,964.84 

271.8388 

5,463-9344 

116,421.46 

17 

35.212.03 

530-35I-94 

255.4006 

5,192.0956 

"0,957.53 

18 

32,963.50 

495  •  1  39-  9  * 

240.2830 

4,936-6950 

105,765.43 

19 

30,857.35 

462.176.41 

226.0584 

4,696.4120!  100,828.74 

20 

28,884.66 

431,319.06 

212.6743 

4,47o-3536     96,132.327 

21 

27,037.00 

402.434.40 

200.3587 

4,257.6793)     91,661.974 

22 

25,306.24 

375,397-40 

188.7558 

4,057.3206 

87,404.294 

23 

23.685.06 

350,091.16 

177.8245 

3,868.5648 

83-346-974 

24 

22,166.57 

326,406.10 

167.5260 

3,690.7403 

79,478.409 

25 

20,744-33 

304,239-53 

157.8236 

3,523.2143 

75,787.669 

26 

19,412.30 

283,495-20 

148.8902 

3,365-3907 

72,264.454 

27 

18,164.60 

264.082.90 

140.4624 

3,216.5005 

68,899.064 

28 

16,995.72 

245.918.30 

132.5117 

3,076.0381 

65,683-563 

29 

15,901.41 

228,922.58 

125.1852 

2.943-5264 

62,607.525 

30 

14,876.14 

213,021.17 

118.2635 

2,818.3412 

59,663.999 

31 

i3-9'5-S4 

198.145.03 

111.7243 

2,700.0777 

56,845.658 

32 

13,016.42 

184,229.19 

105.6926 

2,588.3534 

54,145.580 

33 

12,173-95 

171,212.77 

100.1237 

2,482.6608 

51,557.226 

34 

11,384.72 

159,038.82 

94.84670 

2,382.537! 

49,074-566 

35 

10,645.47 

147,654.10 

89.84627 

2,287.6904 

46,692.029 

36 

9-953-050 

137,008.63 

85-33960 

2,197.8441 

44-404-338 

37 

9-304-330 

127,055.58 

8i.ost;22 

2,112.5045 

42,206.494 

33 

8,696.614 

"7.75I-25 

77.18859 

2,031.4493 

40,093.990 

39 

8,127.166 

109,054.63 

73-49997 

1,954.2607 

38,062.540 

40 

7.593-635 

10,027.47 

70.16506 

1,880.7607 

36,108.280 

4i 

7,093.643 

93.333-S3I 

66.67222 

1,810.5956 

34,227.519 

42 

6.625.144 

86,240.188 

64.07927 

i,743-6234 

32,416.923 

43 

6,186.057 

79,615.044 

61.37623 

i,679-5442 

,30.673.300 

44 

5.774-525 

73.428.987 

58.99186 

1,618.1679 

28,993-756 

45 

5,388.674 

67,6154.462 

56-74930 

i»559-176i 

27,375.5SS 

46 

5.026.906 

62.  26*;.  788 

54.83025 

1,502.4268 

25,816.412 

47 

4,687.532 

57,238.882 

53.06862 

i,447-5965 

24,313-985 

48 

4,369-  *33 

52,551.350 

51.56092 

i,394-5279 

22,866.388 

49 

4,070.263 

48,182.217 

50.32530 

1,342.9670 

21,471.861 

5° 

3-7S9-544 

44,111.954 

49.26926 

1,292.6417 

20,128.894 

5i 

3,525-773 

40.322.410 

48.36477 

i,243-3724 

18,836.252 

52 

3,277-836 

36.796.637 

47-587H 

1,195.0077 

17,592.879 

53 

3,044.711 

33,5.8.801 

46.91461 

1,147.4205 

16.397.872 

54 

2,825.455 

30,474.090 

46.36856 

1,100.5059 

15,250-45! 

OF  LIFE   INSURANCE. 


75 


TABLE  No.  XVII— (CONTINUED.) 
COMMUTATION  COLUMNS,  AMERICAN  EXPERIENCE,  6  PER  CENT. 


% 

^ 

Dx. 

Ak 

Ck 

Mx. 

jR*. 

55 

2,619.154 

27,648.635 

45.88711 

l>  °54-  1373 

14,149.945 

56 

2,  425.013 

25,029.481 

45-49213 

1,008.2502 

13,09^.808 

57 

2,242.257 

22,604.468 

45-13107 

962.75810 

12,087.558 

58 

2.070.205 

20,362.211 

44.79368 

917.62703 

11.124.800 

59 

1,908.230 

18,292.006 

44-50145 

872-83335 

10,207.173 

60 

i>755-7l6 

16,383-776 

44.21317 

828.33190 

9-334-3394 

61 

1,612.122 

14,628.060 

43.92288 

784.11873 

8,506.0075 

6211,476.947 

i3>oi5-933 

43.60014 

740.19585 

7,721.8887 

63 

I.349-746 

11,538.991 

43.22123 

696-59571 

6,981.6929 

64 

1,230.124 

10,189.245 

42.79084 

653-3744S 

6,285.0972 

65 

1,117.703 

8,959.121 

42.31342 

610.58364 

5,631.7227 

66 

1,012.124 

7.841.418 

41.73278 

568.27022 

5,021.1391 

67 

913.1013 

6,829.2936 

41.04427 

526.53744 

4,452.8688 

68 

820.3721 

5,916.1923 

40.24618 

485-493I7 

3.926.3314 

69 

733-6S97 

5,095.8202 

39.28841 

445.24699 

3,440.8382 

70 

652.8716 

4,362.1305 

38.18240 

405-95858 

2,995-59" 

7i 

577-7344 

3,709.2589 

36.87985 

367.77618 

2,589-6327 

72 

508.1524 

3.I3I-5245 

35-34659 

330.89633 

2,221.8565 

73 

444.0425 

2,623.3721 

33-58719 

295-54974 

1,890.9601 

74 

385-3208 

2,179.3296 

31-63543 

261.96255 

1,595.4104 

75 

33I-8748 

1,794.0088 

29.54641 

230.32712 

.!,  333-4479 

76 

283-5430 

1,462.1340 

27-36739 

200.78071 

1,103.1207 

77 

240.1261 

1,178.5910 

25-15983 

173-4I332 

902.3400 

78 

201.3741 

938.4649 

22.95417 

148.25349 

728.92670 

79 

167.0214 

737.0908 

20.75693 

125.29932 

580.67321 

So 

136.8105 

570.0694 

18.64571 

104.54239 

455-37389 

Si 

110.4208 

433-2589 

16.52192 

85.89668 

350.83150 

82 

87.64860 

322.83809 

14.41216 

69-37476 

264.93482 

§3 

68.27522 

235-  18949 

12.33856 

54.96260 

195.56016 

84 

152.07201 

166.91427 

10.38290 

42.62404 

HO-  59756 

85 

38-74165 

114.84226 

8.609106 

32.241142 

97-973523 

S6 

27.93962 

76.10061 

7.002851 

23-632036 

65-7323Si 

87 

i9-35528 

48.16099 

5-533062 

16.629185 

42.100345 

88 

12.72664 

28.80571 

4.162468 

11.096123 

25.471160 

89 

7.843789 

16.079072 

2.929308 

6-933655 

I4-375037 

90 

4.470494 

8.235283 

1.917022 

4.004347 

7.441382 

91 

2.300426 

3.764789 

1.155568 

2.087325 

3-437035 

92 

1.014645 

i-464363 

.6071208 

•9317566 

1.3497102 

93 

.3500915 

.4497184 

.2424804 

•3246358 

•4179536 

94 

.0877947 

.0996269 

.0709930 

.0821554 

•0933  '  78 

95 

.0118322 

.0118322 

.0111624 

.0111624 

.0111624 

76 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XVIII. 
NET  PREMIUMS  PER  $1,000,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Single 
lift. 

Whole 
life. 

Ten 
payment 
life. 

Endow- 
ment 10 
years. 

Endow- 
ment   15 
years. 

Endow-  Endo-i'- 
ment    20  ment    25 
years,      years. 

Endow- 
ment  30 
years. 

Endow- 
ment 35 
years. 

20 
21 

22 

23 
24 

25 
26 

27 
28 
29 
30 
31 
32 

33 
34 

3I 
36 

37 
38 
39 
40 
4i 
42 
43 
44 

4? 
46 

47 
48 
49   * 
50 
5'i 
52 
53 
54 
55 
56 
57 
58 

I9 
60 

61 
62 

? 
64 

65 
66 

67 
68 
69 
70 

217-45 
221.  l6 
225.02 
229.05 
233.26 

237-64 
242.23 
247.01 
25I-99 
257-I9 
262.61 
268.26 
274.16 
280.30 
286.69 

293-35 
300.29 

307-5I 
3I5-03 
322.83 

330-95 

339-37 
348.12 

357-19. 
366.60 

376.35 
386.43 
396-85 
407.60 
418.67 
430-04 
441.70 

453-63 

465.82 
478.26 
490.93 
503.80 
516.87 
530-10 
543-48 
556.99 
570-59 
584.26 

597-97 
61  1.70 
625.42 
639.08 
652-65 
666.11 
679.42 
692.54 

11-97 
12.23 
12.50 
12.79 
13.10 
13.42 
13-77 
I4-I3 
I4-5I 
14.91 

15-34 
15-79 
16.27 
16.77 

I7-3I 
17.88 
18.48 
19.12 
19.81 

20-53 
21.30 
22.12 
23.00 

23-93 

24.92 

25-99 

27.12 

28.33 
29.63 
31.01 

32-49 
34-07 

35-75 
37-55 
39-47 
41-53 
43-72 
46.07 
48-58 
51-27 
54-14 

57-22 

60.52 
64.05 

67.84 

71.90 
76.25 
80.91 

85.91 

91.26 

97.00 

27.17 
27.64 
28.13 
28.64 
29.18 

29-73 
30.32 
30.92 

3J-56 
32.22 
32.92 

33-64 
34-40 

35-19 
36.01 
36.87 

37-77 
38-71 
39-69 
40.72 
41.79 
42.90 
44.07 
45-29 
46.57 
47.90 

49-30 
50.76 
52.29 
53-89 

55-57 
57-3i 

59-  "3 
61.03 
63.02 
65.10 
67.27 

69-55 
71.94 

74-45 
77.08 
79-86 
82.79 
85.89 
89.17 
92.66 

96.35 
100.28 
104.46 
108.90 
"3-63 

81.90 
8l.93 
81.96 
81.99 
82.04 
82.06 
82.10 
82.14 
82.19 
82.24 
82.29 

82-35 
82.41 
82.48 

82.55 
82.64 

82-73 
82.83 
82.94 
83.07 
83.21 
83-36 
83-54 
83-74 
83-97 
84.23 
84.52 
84.86 
85.24 
85.67 
86.17 
86.69 
87.30 
87.97 
88.73 
89.55 
90.48 

9r-5i 
92.65 

93-92 
95-33 
96.90 
98.64 
100.58 
102.52 
104.49 

50-55 
50.58 
50.62 
50.66 
50.70 
50-75 
50.80 
50.85 
50.91 

50.97 
51.04 
51.12 
51.20 
51.29 
51-39 
5I-5I 
5I-63 
51-77 
5I-92 
52.10 

52.30 
52.52 
52.77 
53-05 

53-37 
53-73 
54-  H 
54.60 

55-13 
55-71 
56.36 
57-09 
57-9° 
58.80 
59.80 
60.92 
62.15 

63-53 
64.05 
66.74 
67.61 
70.69 
72-95 
75-47 
78.23 
81.24 

35-43 
35-47 
35-52 
35-57 
35-62 
35-68 
35-74 
35-Si 
35-89 

2r22 

36.06 

36.16 
36.27 

36.39 
36.52 
36.68 
36.85 
37-04 
37-25 

37-49 
37-76 
38.06 
38.40 

38.79 
39.22 

39-70 

40.25 
40.86 

4l-52 

42.30 

43-15 
44.09 

45-H 

46.30 

4758 
49.00 

50.57 
52.29 

54.t9 
-6  ->8 

26.80 
26.86 
26.91 
26.98 
27.05 
27.12 
27.20 
27.28 
27.38 
27.48 
27.61 
27.74 
27.89 
28.05 
28.24 
28.44 
28.67 
28.93 
29.21 

29-53 
29.90 

30-29 
30.74 
31-24 
31.81 

32.43 
33-13 
33-90 
34-77 
35-74 
36.79 
37.96 
39-25 
40.66 
42.22 
43-91 

21.42 
21.49 
21.56 
21.64 
21.72 
21.82 
21.93 
22.04 
22.l6 
22.31 
2247 
22.64 
22.84 
23.06 
23-30 
23-57 
23-87 
24.21 
24.58 
25.00 
25.46 

25-97 
26.54 
27.18 
27.88 
28.65 

29-5I 
30.46 

3J-5° 

32.64 

33-89 

17.89 

1/-97 
18.07 
18.17 
18.28 
18.41 

18.55 
18.70 
18.87 
19.05 
19.26 
19.49 
19.74 
20.03 
20.34 
20.68 
21.07 
21.49 
21.96 
22.48, 

23-05  ; 
23-68 

24-37 
25.10 
25.96 
26.87 

.... 

58.57 

1 

OF  LIFE   INSURANCE. 


,  I 


TABLE   No.  XIX. 

NET  ANNUAL   PREMIUMS   PER   $1,000,   COMBINED   EXPERIENCE,  4 

PER  CENT. 


Affe. 

Single 
life. 

Whole 
life. 

Ten 
payment, 
life. 

Endow- 
ment, IO 
years. 

Endow- 
ment, 15 
years. 

Endow- 
ment, 20 
years. 

Endow- 
ment, 25 
years. 

Endow- 
ment, 30 
y.ars. 

20 
21 

22 
23 
24 
25 
26 

27 
28 

29 
30 
31 
32 

33 
34 

3£ 
36 

37 
38 

39 
40 

42 
43 
44 
45 
46 

251.91 
256.56 
261.37 
266.36 
271.50 
276.82 
282.31 
287.99 
293.86 
299.91 
306.17 
312.63 
319.29 
326.17 

333-27 
340.60 

348-17 
355-99 
364.07 

381.04 
389.96 
399.18 
408.71 
418.52 

428-57 
478.86 

12.95 

13.27 
13.61 
13.96 

H-33 

14.72 

15-13 
15-56 

16.01 
16.48 
16-97 
17.49 
18.04 
18.62 
19.23 
19.87 
20.54 
21.26 
22.02 
22.82 
23-68 
24-59 
25-55 
26.58 
27.68 
28.85 

3O  08 

30.81 
31.40 
32.00 
32-63 
33-27 
33-94 
34-64 
35-35 
36.09 
36.86 
37-66 
38.48 

39-33 
40.21 
41.12 
42.06 
43-04 
44-05 

46.20 
47-33 

48.53 
49-77 
51.08 

52-44 
53-86 

CC   37 

83-87 
83.91 

83-97 
84.02 
84.08 
84.15 
84.22 
84.29 
84-37 
84-45 
84-54 
84.63 
84.71 
84.82 
84-93 
85-03 
85-I5 
85.28 
85.42 

8^76 

85.97 
86.22 

86.51 

86.84 

87.02 
87  61 

52.27 
52.33 
52.40 
52-47 

52-54 
52.62 

52.70 

52-79 
52.88 

52.98 

53-oS 
53-20 

53-43 
53-57 
53-72 
53-88 
54-07 
54-27 
54-51 
54-77 
55-07 
55-40 

55-79 
56-23 
56.70 

C7  22 

36.97 
37-05 

37-12 
37-21 
37-29 
37-38 
37-48 
37-59 
37-7° 
37-82 

37-95 
38.09 

38-25 
38.41 

38.59 
38.80 

39-02 
39.28 
39-55 
39-87 
40.22 
40.60 
41.05 

41-53 
42.08 
42.68 

47    74 

28.19 
28.28 
28-37 
28-47 
28-57 
28.68 
2S.SI 
28.94 
29.08 
29.24 
29.40 

29-59 
29.79 
30.04 
30.26 
30.52 
30-Sl 
3I-H 

31.90 

32-35 
32.84 

33-38 
34-00 

34-67 
35-42 
7fi  27 

22.68 
22.79 
22.90 
23.01 

23-I5 
23.29 

23-44 
23.61 

23-79 
24.00 
24.21 
24.44 
24.70 
24.98 
25.29 

26.OI 
26.42 
26.87 

27-37 
27.92 

28-53 
29.20 
29.94 
30.76 

47 

44Q.7C 

71  7Q 

c6  85 

88  06 

C7  80 

77    12 

48 

460.02 

32.77 

cS  43 

88  c5 

cS  43 

44.  Rtr 

78  OS 

4O 

470.88 

34  ">7 

80  O7 

45-71 

5O 

481.01 

95.78 

6l.74 

89.66 

50.86 

46.65 

40.  27 

CI 

4Q3.  II 

37  41 

67  4O 

oo  20 

60  68 

47-68 

52 

CO4.46 

7Q.IC 

6c  70 

OO  O7 

61  c.7 

48.81 

53 

4I.OO 

67.17 

QI.73 

62  cc 

50.03 

C27.  C7 

42  OC 

69   12 

02  cc 

51-37 

cc 

C7Q.7I 

4C.O2 

71   14 

O7  4C 

64  80 

152.84 

56 

47.23 

73.25 

Q4  43 

66  09 

563.  io 

4O  C7 

*7C  44 

OC    CI 

67    CT 

58 

C7C.  14. 

C2.O7 

77  7  c 

06  74 

587.26 

C.4.72 

So  15 

Q7  QQ 

7O  77 

6O 

5QQ.43 

C.7.C.6 

82  68 

QQ.47 

72.64 

61 

6  1  1  .63 

60.  C.7 

S^-34 

IOI.O7 

62 

623.83 

6*.  78 

88.13 

IO2  Si 

63 

635.00 

67.2O 

QI  O7 

IO4.73 

64 

6.48.12 

7O.84 

Q4.  I  6 

106.83 

65 

660.17 

74-72 

97  4  } 

log  12 

66 

672.13 

78.84 

loo  88 

67 

683.06 

83.24 

IO4   C7 

68 

6Q  $  .  65 

87.01 

1  08  59 

69 

7O7.IQ 

02.  8q 

I  12  48 

70 

718.57 

98.20 

II6.S5 

78  PRINCIPLES  AND  PRACTICE 

TABLE   No.  XX. 
NET  ANNUAL  PREMIUMS  PER  $1,000  FOR  TERM  INSURANCE  POLICIES. 


Age. 

AMERICAN  EXPERIENCE,  4^  PER  CENT. 

COMBINED  EXPERIENCE,  4  PER  CENT. 

Three 
years. 

Five 
years. 

Seven 
years. 

Ten 

years. 

Three 
years. 

Five 
years. 

Seven 
years. 

Ten 

years. 

20 

7-50 

7-55 

7.61 

7-68 

7.09 

7.18 

7.27 

7.41 

21 

7-57 

7.61 

7.66 

7-74 

7.18 

7-27 

7-36 

7-51 

22 

7.62 

7.67 

7.72 

7.80 

7-27 

7-37 

7-47 

7-63 

23 

7.67 

7.72 

7.78 

7.87 

7-37 

7-47 

7-58 

7-75 

24 

7.72 

7.78 

7.84 

7-94 

7-47 

7-58 

7.69 

7.87 

25 

7.78 

7.84 

7.91 

8.01 

7-58 

7.70 

7-82 

8.01 

26 

7.84 

7.91 

7-98 

8.10 

7.70 

7.82 

7-95 

8.15 

27 

7.91 

7.98 

8.06 

8.19 

7-82 

7-95 

8.09 

8.30 

28 

7-99 

8.06 

8.15 

8.28 

7.96 

8.09 

8.24 

8.46 

29 

8.07 

8.15 

8.24 

8-39 

8.10 

8.24 

8-39 

8.62 

30 

8.15 

8.24 

8-34 

8.50 

8.25 

8.40 

8.^6 

S.So 

31 

8.24 

8-33 

8.44 

8.63 

8.41 

8-57 

8-73 

8.98 

32 

8-34 

8.45 

8-57 

8.77 

8-57 

8.74 

8.91 

9.17 

33 

8-45 

8-57 

8.69 

8.91 

8-75 

8.92 

9.10 

9-38 

34 

8-57 

8.70 

8.84 

9.08 

8-93 

9.11 

9-3o 

9-59 

35 

8.70 

8.84 

9.00 

9.26 

9.12 

9-3i 

9-50 

9-83 

36 

8.84 

9.00 

9.17 

9-47 

9-3i 

9-5i 

9.72 

10.  10 

37 

9.00 

9.18 

9-36 

Q.  70 

9-52 

9-73       9-96 

10.41 

38 

9.18 

9-37 

9-58 

9-94 

9-74 

9.96 

10.23 

10.75 

39 

9-37 

9-58 

9.81 

10.22 

9.96 

1O.2I 

10.53 

11.15 

40 

9-58 

9.81 

10.08 

10.54 

10.21 

10.  <;i 

10.89 

"•59 

4i 

9.81 

10.07 

Jo-37 

lO.gO 

10-49 

10.86 

11.31 

12.09 

42 

10.07 

10.36 

10.70 

11.29 

10.83 

11.28 

11.80 

12.67 

43 

10.37 

10.69 

11.08 

11.77 

11.25 

11.77 

12.35 

13-30 

44 

10.69 

11.07 

11.50 

12.29 

11.76 

12.34 

12.98 

14.03 

45 

11.06 

11.50 

12.00 

12.88 

12-34 

12.98 

13.68 

14.81 

46 

11.49 

11.99 

12-57 

13-55 

12-99 

13.69 

1  4-  45 

15.69 

47 

11.98 

12-55 

'3-19 

14.30 

I3-7I 

14-47 

15-29 

16.63 

48 

12.55 

13-19 

13-91 

15-13 

14.48 

i5-3i 

16.20 

17-65 

49 

I3-I9 

13-91 

14-73 

16.07 

I5-32 

16.23 

17.20 

18.76 

5° 

13.92 

14.72 

15.60 

17.12 

16.24 

17-23 

18.28 

19.97 

5* 

1  4-  73 

15.62 

16.62 

18.28 

I7-25 

18.31 

'9-45 

21.28 

52 

15-63 

16.63 

17-73 

19.56 

18.34 

19.50 

20.72 

22.71 

53 

16.64 

17-75 

18.97 

20.98 

19-53 

20.78 

22.10 

24.27 

54 

17.77 

19.00 

20.34 

22.56 

20.81 

22.16 

23.60 

25.96 

55 

19.02 

20.38 

21.86 

24.29 

22.21 

23.67 

25-24 

27.80 

56 

20.40 

21.91 

23-54 

26.20 

23-7I 

25-3I 

27.03 

29.81 

57 

21.94 

23.60 

25-39 

28.31 

25-35 

27.10 

28.99 

32.00 

58 

23.64 

25-47 

27.44 

3°-63 

27-I5 

2Q.08 

31-13 

34-39 

59 

25-52 

27-54 

29.60 

33-iS 

29.13 

3^24 

33-47 

36-99 

60 

27.60 

29.82 

32.19 

35-99 

31-31 

33-62 

36.04 

39.81 

_.    __ 

VALUATION   TABLES. 


NET  VALUES. 

The  following  tables,  from  page  82  to  119  give  the  net  values 
of  a  policy  of  $1,000,  according  to  various  plans  of  insurance 
and  ages,  and  also  according  to  the  two  standards  of  mortality 
and  interest  generally  adopted  in  the  United  States. 

The  states  of  New  York,  California,  Kansas,  Kentucky,  Mis- 
souri, Michigan,  and  Wisconsin,  have  adopted  the  American 
Experience  Table  and  44  per  cent  interest,  while  Massachusetts, 
Connecticut,  Maine,  New  Hampshire  and  Illinois,  use  the  Com- 
bined Experience  4  per  cent. 

The  net  values  are  given  to  the  end  of  each  policy  year,  to  the 
1 5th  and  also  of  the  2Oth  year,  where  the  number  of  annual 
premiums  is  sufficient. 

Although  there  has  been  an  endless  amount  of  discussion 
about  the  relative  merits  of  the  two  standards  of  valuation,  very 
few  persons  have  taken  the  trouble  to  investigate  for  themselves 
the  actual  difference  there  is  between  the  valuations  of  the 
same  policy  made  upon  both  of  them.  Thus  the  value  of  a 
whole  life  policy  issued  at  age  20,  and  having  been  in  force 
5  years,  has  a  value  29  per  cent  greater  by  the  Combined  Ex- 
perience 4  per  cent  standard  than  by  the  other.  In  the  older 
ages,  and  when  the  policy  has  been  in  existence  a  greater  num- 
ber of  years  this  difference  diminishes.  A  life  policy  with  the 
same  conditions,  issued  at  age  35,  has  a  reserve  15  per  cent 
greater  by  the  Combined  Experience  4  per  cent  table,  and  at  50 
only  4  per  cent  greater.  Also,  the  longer  a  policy  is  in  force 
the  less  the  difference,  and  we  see  that  a  policy  issued  at  age  50, 
and  in  force  20  years,  has  a  larger  reserve  by  the  American  Ex- 
perience 4^  per  cent  standard  than  by  the  other.  Similar  differ- 
ences, though  in  a  less  degree,  are  seen  in  the  Ten  payment  Life 
and  Endowment  policies. 

The  difference  in  the  valuation  of  endowments  by  the  two 
standards  is  very  slight.  In  the  Ten  Year  Endowments  it  is 
almost  nothing,  but  increases  with  the  length  of  the  policy  term. 


OF  LIFE  INSURANCE. 


8l 


TABLE  NO.  XX.  a. 

SHOWING  THE  DIFFERENCE  BETWEEN  THE  VALUES  OF  THE  SAME  POL- 
ICY  ACCORDING   TO   THE    AMERICAN    EXPERIENCE   $\   PER   CENT,    AND 

THE  COMBINED  EXPERIENCE,  4  PER  CENT.  STANDARDS. 


WHOLE  LIFE. 

FIFTEEN-  YEAR  ENDOWMENT. 

Age  SO. 

Age  2O. 

Vf 

1? 

Premium 
American 
Experience, 
4/^  /""  <«»*• 

Premium 
Combined 
Experience, 
4  per  cent. 

Ratio. 

*& 
g 

Premium, 
American 
Experience, 
tf/2  per  cent. 

Premium, 
Combined 
Experience, 
4  per  cent. 

Ratio. 

i 
5 

10 

15 

20 

4-74 
25.81 

57-71 
97.00 
145.04 

6.22 
3330 
7253 
118.56 
I72.6l 

I-3I 
1.29 
1.26 
1.22 
X.ZQ 

I 

5 

10 

45-37 
251.86 

577-52 

47-42 
26o.OI 
586.80 

1.045 
1.032 

1.016 

Age  35. 

Age  35. 

I 
5 

10 

45-27 
251.09 

575-69 

47-02 
257-94 

583.58 

1.039 

1.027 

1.013 

I 

5 

10 

15 

20 

982 
53-20 

"7-45 
193.42 

279-59 

11.48 
61.34 

I33-4I 
214.30 

301-35 

I.I7 
I-I5 
1-13 
I.  II 

1.08 

Age  BO. 

I 

5 
10 

45-74 
250.28 
568.47 

47.07 
254.64 

572.42 

1.029 

1.013 

1.007 

Age  5O. 

I 

5 

10 

15 

20 

20.45 
106.83 
222.74 

342-79 
460.56 

21.62 
110-79 
226.84 
344-07 
456.79 

1.05 
1.04 
i.  02 

I.OO 

•99 

TWENTY-  YEAR  EI'DOWMENT. 

Age  2O. 

I 
5 

10 

29-45 
163.27 
373-82 

31-39 
171.80 

386.71 

1.  066 

1.052 
1.035 

TEN  PAYMENT  LIFE. 

Age  35. 

Age  2O. 

I 

5 
10 

29.64 
163.81 
373-59 

3I-36 
171.29 

385.17 

1.058 
1.045 
1.031 

I 
5 

20.75 
114.91 

24.94 
136.30 

i.  20 

I  JO 

Age  35. 

Age  5O. 

I 

5 

29.85 
164.99 

34-78 
190.23 

1.16 
i-i5 

I 
5 

10 

3i-74 
170.88 
377.08 

33-" 

175-76 
382.92 

1.043 
1.028 
1.015 

Age  5O. 

I 

5 

449° 
245-54 

4906 
265.87 

1.09 
1.08 

TWENTY-FIVE-YEAR  ENDOWMENT. 

Age  2O. 

TEN-  YEAR  ENDOWMENT. 

I 

5 

10 

2  '.36 

112.72 
257-57 

22.19 
121.18 
271.90 

1.089 
1-075 

1.056 

Age  2O. 

I 
5 

7».39 
4.35-59 

80.51 
442.17 

1.027 

1.  01? 

Age  35. 

Age  35. 

I 
5 

10 

20-95 

115-33 
261.32 

22.67 
123.21 
275.11 

1.082 
1.068 
1.052 

I 
5 

78.10 
434-32 

78.89 

439-79 

I.OIO 

1.013 

Age  5O. 

Age  5O. 

I 

5 
10 

25.00 
132.64 
284.94 

26-36 
137-64 
29T-35 

1.054 

1.038 

I.O22 

I 

5 

77-31 
42938 

78.56 
432.60 

1.016 

i.  008  : 

S2 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXI. 


NET  VALUE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  AT  THE  END  OF 
VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

4-74 

9.68 

14.83 

20.20 

25.81 

31.66 

37-77 

44.14 

21 

4.96 

10.14 

15-54 

21.17 

27.06 

33-19 

39-59 

46.17 

22 

5.20 

10.63 

16.29 

22.2O 

28.37 

34-80 

4I-5I 

48.51 

23 

5-46 

11.15 

17.09 

23.29 

29.76 

36.50 

43-53 

50.86 

24 

5-72 

11.70 

17-93 

24-43 

31.22 

38-29 

45-66 

53-34 

25 

6.01 

12.28 

18.82 

25.64 

32-75 

40.16 

47.89 

55-95 

26 

6.31 

12.83 

19-75 

26.90 

34-36 

42.13 

50.24 

58.68 

27 

6.62 

13-53 

20.72 

28.23 

36.06 

44.21 

52-71 

61-SS 

28 

6-95 

14.20 

2i-75 

29.63 

37-85 

46.39 

55-30 

64-58 

29 

7-30 

14.91 

22.84 

31.11 

39-72 

48.69 

58-03 

67-75 

30 

7.66 

15-66 

23-99 

32.66 

41.69 

51.11 

60.90 

71.09 

31 

8.06 

16.45 

25.19 

34-29 

43-78 

53-64 

63.91 

74-58 

32 

8.46 

17.27 

26.45 

36.01 

45-96 

56-3I 

67.06 

78.24 

33 

8.89 

18.14 

27.79 

37.82 

48.26 

59.10 

70-37 

82.08 

34 

9-34 

19.07 

29.19 

39-72 

50.67 

62.04 

73-85 

86.11 

35 

9.82 

20.04 

30.67 

41.72 

53-20 

6^.12 

77-50 

90-34 

36 

10.32 

21.06 

32.21 

43.81 

55-84 

68.34 

81.31 

94-77 

37 

10.85 

22.12 

33-84 

46.00 

58-63 

71-74 

85-33 

99.40 

38 

11.40 

23.24 

35-54 

48.31 

61.56 

75-30 

89.52 

104.25 

39 

11.98 

24.42 

37-34 

50-74 

64.64 

79-03 

93-92 

109.30 

40 

12.59 

25.66 

39-23 

53-29 

67.86 

82.93 

98.50 

"4-57 

4i 

13.24 

26.98 

41.23 

55-97 

71.24 

87.01 

103.28 

120.04 

42 

13.92 

28.36 

43-3i 

58.78 

74.76 

91.25 

108.23 

125.67 

43 

14.64 

29.80 

45-49 

61.70 

78.42 

95-64 

"3-33 

131.46 

44 

I5-38 

31-3I 

47-75 

64.72 

82.20 

100.15 

118.56 

137-39 

45 

16.17 

32.87 

50.11 

67.86 

86.09 

104.78 

123.92 

143-47 

46 

16.98 

34-50 

52-54 

71.07 

90.07 

109.51 

129.39 

149.66 

47 

17.82 

36.18 

55-03 

74-35 

94.14 

"4-35 

134-98 

155-98 

48 

18.69 

37-88 

57-56 

77.70 

98.28 

119.28 

140.66 

162.40 

49 

19.56 

39.61 

60.14 

8i.ii 

102.51 

124.30 

146.45 

168.92 

50 

20.45 

4i-39 

62.78 

84.61 

106.83 

129.42 

152-34 

I75-56 

5i 

21-37 

43.21 

65-49 

88.18 

111.24 

134.64 

158-35 

182.32 

52 

22.32 

45.08 

68.27 

91.83 

"5-75 

139-97 

164.46 

189.18 

53 

23.29 

47.00 

71.11 

95-56 

120.34 

145-39 

170.67 

196.14 

54 

24.28 

48.96 

74-00 

99-36 

125.01 

150.90 

176.97 

203.17 

55 

25-30 

50.96 

76.95 

103.24 

129.77 

156.49 

183-34 

210.28 

56 

26.33 

53-oo 

79-97 

107.19 

134.60 

162.15 

189.79 

217-45 

57 

27-39 

55-09 

83-05 

in.  20 

I39-50 

167.88 

196.29 

224.68 

58 

28.48 

57-22 

86.17 

115.26 

144.44 

173.66 

202.84 

231.92 

59 

29.58 

59-38 

89.32 

119.36 

H9-43 

179-47 

209.40 

239-14 

60 

30.70 

61.56 

92.51 

123-50 

154.46 

185.29 

215.94 

246-33 

OF  LIFE  INSURANCE. 


TABLE  No.  XXI— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  AT  THE  END  OF 
VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thirfnth 
year. 

Fourt'nlh 
year. 

Fifteenth 
year. 

Twentieth 
year. 

20 

50.78 

57-71 

64-93 

72.46 

80.31 

88.49' 

97-00 

145.04 

21 

53-  -3 

60.48 

68.05 

75-94 

84-I5 

92.70 

IOI.OZ 

151.78 

22 

5  5.  So 

63.40 

71-33 

79-58 

88.18 

97-13 

106.45 

158.84 

23 

5$-  5  1 

66.47 

74-77 

83.41 

92.41 

101.78 

111.52 

166.21 

24 

6i-35 

69.69 

7S-3S 

87-43 

96-85 

106.65 

116.83 

J73-91 

25 

64-34 

73.08 

82.18 

91.65 

101.51 

111-74 

122.39 

181.94 

26 

67.47 

76.63 

86.  1  6 

96.07 

106.37 

117.08 

128.19 

190.30 

27 

70.77 

80.36 

9°-34 

100.70 

111.48 

122.66 

134.28 

199.00 

28 

74-23 

S4-27 

94.71 

105.56 

116.82 

128.51 

140.64 

208.03 

29 

77.86 

88-37 

99.29 

110.63 

122.41 

134-63 

147-30 

217-39 

30 

81.67 

92.67 

104.10 

115-96 

128.26 

141.03 

154.24 

227.05 

31 

85.67 

97.l8 

109.13 

121-53 

I34.40 

147.71 

161.49 

237.02 

32 

89.84 

101.90 

114.40 

127-37 

140.79 

154.69 

169.04 

247.26 

33 

94-23 

106.84 

119.92 

I33-46 

147-47 

161.94 

176.88 

257-78 

34 

98-83 

112.03 

125.69 

139-83 

I54.43 

169.50 

185.02 

268.56 

35 

103.66 

"7-45 

131.72 

146.46 

161.67 

177-34 

193.43 

279-59 

36 

108.69 

123.11 

137-99 

153-36 

169.18 

185.43 

202.09 

290.85 

37 

113.96 

129.01 

ifl-53 

160.51 

176.93 

193.77 

211.  OO 

302.32 

38 

"9-45 

I35-I5 

i5i-3i 

167.91 

184.92 

202.34 

22O.I4 

3I3-99 

39 

125.18 

141.52 

158-31 

175-53 

193-  *s 

211.  IO 

229.53 

325-85 

40 

131.11 

148.11 

165-53 

183-36 

201.59 

220.18 

239.11 

337-86 

4i 

I37-25 

154.89 

I72-95 

191.41 

210.24 

229.41 

248.91 

350.00 

42 

H3-55 

161.86 

180.56 

1  99.64 

219.07 

238.83 

258.87 

362.25 

43 

150.02 

168.99 

188.34 

208.05 

228.08 

248.40 

268.99 

374.58 

44 

156.64 

176.28 

196.28 

216.61 

237-23 

258-13 

279.26 

386.96 

45 

163.41 

183-72 

204.37 

225.32 

246.54 

268.00 

289-65 

399-37 

46 

170.30 

191.29 

212.58 

234-I5 

255-96 

277-98 

300.14 

411.76 

47 

177-33 

198.98 

220.93 

243.12 

265-51 

288.06 

310.72 

424.11 

48 

184.45 

206.79 

229.38 

252.18 

275-14 

298.22 

32L36 

436-38 

49 

191.69 

214.71 

237-94 

261.34 

284.85 

308.44 

332.06 

448.54 

50 

199.04 

222.74 

246.60 

270.59 

294.64 

318.73 

342-79 

460.56 

5i 

206.51 

230.87 

255-36 

279.92 

304-  5  i 

329.07 

353-54 

472.41 

52 

214.08 

239.09 

264.19 

289.32 

314.42 

339-42 

364-27 

484.08 

53 

221.73 

247.40 

273.10 

298.77 

324-34 

349-76 

374-96 

495.61 

54 

229.45 

255-76 

282.05 

308.23 

334-26 

360.05 

385-55 

507.07 

55 

237-25 

264.19 

291.02 

317-69 

344-13 

370.27 

396.04 

518.57 

56 

245.09 

272.62 

299.98 

327.11 

353-92 

38o.37 

406.37 

530-21 

57 

25--9S 

281.06 

308.92 

336.45 

363-61 

390.22 

416.55 

542.08 

58 

260.81 

289.45 

3I7-77 

345-69 

373-15 

400.12 

426.61 

554-26 

59 

268.62 

297-77 

326.51 

354-77 

382-53 

409.80 

436-65 

566.77 

60 

276.36 

305-98 

335-n 

363-7I 

391.81' 

419.47 

446.78 

579.68 

84 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XXII. 

NET  VALUE  PER  $1,000  OF  A  TEN-PAYMENT  LIFE  POLICY,  AT  THE 
OF  VARIOUS  YEARS,   AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

20 

20-75 

42.56 

65.48 

89.58 

114.91 

21 

21.  2O 

43-47 

66.89 

9!-5i 

"7-39 

22 

21.66 

44-43 

68.36 

93-53 

119.98 

23 

22.15 

45-43 

69.90 

95-63 

122.67 

24 

22.66 

46.48 

7I-5I 

97.82 

125.48 

25 

23.19 

47-57 

73-18 

IOO.II 

128.41 

26 

23-74 

48.69 

74.92 

102.48 

131.46 

27 

2432 

49.88 

76.73 

104.96 

I34-63 

28 

24.92 

51.10 

78.62 

107-54 

137-94 

29 

25-54 

52-38 

80.59 

110.23 

141.38 

30 

26.19 

53-72 

82.63 

113.02 

144-95 

31 

26.87 

55-10 

84.76 

115.92 

148.67 

32 

27.58 

56.54 

86.96 

118.94 

I52-53 

33 

28.30 

58.02 

89.26 

122.07  • 

156-54 

34 

29.06 

59-58 

91.64 

125.32 

160.69 

35 

29.85 

61.20 

94.12 

128.68 

164.99 

36 

30.66 

62.86 

96.66 

132.17 

169.45 

37 

3I-5I 

64.58 

99-31 

J35-77 

174.06 

38 

32-38 

66.36 

102.03 

139-49 

178-83 

39 

33-28 

68.20  * 

104.86 

143-35 

183.76 

40 

34-21 

70.11 

107.78 

H7-33 

188.84 

4i 

35-i8 

72.08 

no.Si 

i5i-44 

194.09 

42 

36-17 

74.12 

113.91 

155-66 

199.46 

43 

37.20 

76.20 

117.10 

!59-99 

204.98 

44 

38-25 

78-34 

120.36 

164.41 

210.60 

45 

39-33 

80.53 

123.70 

168.93 

216.32 

46 

40-43 

82.76 

127.08 

173-49 

222.09 

47 

4i-55 

85.02 

130.49 

178.09 

227.92 

48 

42.67 

87.28 

I33-9I 

182.72 

233-78 

49 

43-79 

89-53 

137-33 

187-33 

239.66 

50 

44.90 

91.98 

140.76 

191.96 

245-54 

5i 

46.02 

94.04 

144.18 

196.58 

251.41 

52 

47-13 

96.28 

I47-58 

201.17 

257-25 

53 

48.24 

98.50 

150-95 

205-73 

263.04 

54 

49-32 

100.70 

I54-27 

210.22 

268.76 

55 

50-39 

102.85 

157-53 

214.64 

274-39 

56 

51-44 

104.96 

160.73 

218.95 

279.89 

57 

52.46 

107.02 

163-85 

223.17 

285.25 

58 

53-47 

109.02 

166.86 

227.23 

290.42 

59 

54-42 

110.93 

169.74 

231.11 

295-39 

60 

55-33 

112.75 

172.48 

234.82 

300.13 

OF  LIFE  INSURANCE. 


TABLE  No.  XXII— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TEN-PAYMENT  LIFE  POLICY,  AT  THE  END 
OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Sixth 
year. 

Seventh 
year. 

Eighth 

year. 

Ninth 
year. 

Tenth 
year. 

2O 

141.56 

169.57 

199.03 

230.02 

262.61 

21 

144.61 

173.22 

203.32 

234-97 

268.26 

22 

H7-79 

I77-03 

207.79 

240.13 

274.16 

23 

151.11 

iSl.OO 

212.44 

245-5I 

280.30 

24 

I54-56 

185.14 

217.30 

25  1  .  1  2 

286.69 

25 

158.17 

189.46 

222.36 

256.96 

293-35 

26 

161.92 

193-95 

227.62 

263.04 

300.29 

27 

165-83 

198.62 

233.10 

269.37 

307-5I 

28 

169.89 

203.48 

238.81 

275-95 

3I5-03 

29 

174.12 

208.55 

244.74 

282.80 

322.83 

30 

178.52 

213.81 

250.91 

289.92 

330-95 

31 

183.09 

219.28 

257-3I 

297-3I 

339-37 

32 

187.84 

224.95 

263.96 

304-97 

-  348.12 

33 

192.76 

230.83 

270.85 

312.93 

357-19 

34 

197.87 

236.93 

278.00 

32I.I8 

366.60 

35 

203-  T5 

243-25 

285.40 

329-73 

376.35 

36 

208.63 

249.80 

293.08 

338.57 

386.43 

37 

214.21 

256.57 

301.00 

347-72 

396-85 

38 

220.15 

263.57 

309.19 

357-15 

407.60 

39  . 

226.20 

270.79 

3I7-64 

366.88 

418.67 

40 

232.44 

278.22 

326.33 

376.88 

430.04 

4i 

238.85 

285-87 

335-25 

387-I4 

441.70 

42 

245.44 

293.70 

344-38 

397-63 

453-63 

43 

252.17 

301.70 

353-70 

408.34 

465.82 

44 

259-03 

309.84 

363-I8 

419.25 

478.26 

45 

265.99 

318.10 

372.83 

430.36 

490.93 

46 

273-03 

326.48 

382.60 

441.63 

503-80 

47 

280.15 

334-94 

392-49 

453-04 

516.87 

48 

287.31 

343-46 

402.46 

464-57 

53°-  I0 

49 

294.49 

352.02 

412.50 

476.21 

543-48 

5" 

301.68 

360.61 

422.58 

487.92 

556.98 

5i 

308.87 

369.20 

432.69 

499.67 

570.59 

52 

316.03 

377-77 

442.78 

511.46 

584.26 

53 

323-13 

386..J8     iy2.84 

523-23 

597-97 

54 

330.  16 

394-71 

462.82 

534-95 

611.70 

55    337-07 

403-03 

472.69 

546.60 

625.43 

56 

313-84 

411-19 

482.43 

558.14 

639.08 

57 

3.SO-44 

419.17 

491.98 

569-53 

652.65 

58 

35683 

426.94 

501.31 

580.73     666.11 

59 

362.99 

434-4* 

5«>-36 

191  -(ft 

679.43 

60 

368.86 

441-60 

5I<).II 

602.34 

69254 

86 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXIII. 


NET  VALUE  PER$I.OOO  OF  A  TEN- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OP    VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Aff*. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

20 

78.39 

160.91 

247.78 

339-26 

435-59 

21 

78.39 

160.90 

247.76 

339.22 

435-55 

22 

78.37 

160.87 

247.72 

339-17 

43549 

23 

78.34 

160.82 

247.68 

339-  i  2 

435-43 

24 

78.32 

160.78 

247.63 

339.06 

435-36 

25 

78.31 

160.76 

247.58 

339-00 

435-29 

26 

78.29 

160.71 

247-53 

338.94 

435-22 

27 

78.27 

160.68 

247.48 

338.88 

435-4 

28 

78.26 

160.65 

247.42 

338.82 

435-o6 

29 

78.23 

160.61 

24737 

338-74 

434-9S 

30 

78.22 

160.58 

247-3I 

338.66 

434-89 

31 

78.20 

160.53 

247.25 

338.58 

434-79  . 

32 

78.17 

160.49 

247.18 

338-49 

434-68 

33 

78.14 

160.42 

247.11 

338.40 

434-56 

34 

78-12 

160.38 

247.03 

338.29 

434-44 

35 

78.10 

160.33 

246.94 

338.18 

434-32 

36 

78.07 

160.^6 

246.84 

338.05 

434.18 

37 

78.03 

160.18 

246.73 

337-91 

434-02 

38 

77-99 

160.  1  1 

246.62 

337-75 

433-83 

39 

77-95 

160.02 

246.50 

337-6o 

433-64 

40 

77.91 

159.96 

246.38 

337-44 

433-44 

4i 

77-88 

159.88 

246.25 

337-27 

433-21 

42 

77-83 

I59-78 

246.  1  1 

337-07 

432-95 

43 

77-79 

I5Q-68 

245.96 

336.85 

432.67 

44 

77-75 

159.60 

245.81 

336-64 

432.45 

45 

77.72 

I59-50 

245.64 

336-41 

432.11 

46 

77-65 

15937 

24544 

336  13 

43L76 

47 

77-59 

159.20 

245.18 

335-76 

431.29 

48 

77-52 

159-05 

244.85 

335-31 

430.72 

49 

77-43 

158.84 

244.50 

334-So 

430.  10 

50 

7'7-3i 

is8.$8 

244.10 

33424 

429-38 

5i 

77-15 

158-28 

243-63 

333  59 

428.54 

C2 

77-Qi 

15793 

243.09 

33^88 

427.58 

53 

76.84 

I57-56 

242.47 

33I-96 

426.53 

54 

76.63 

157.12 

241.81 

33i-o8 

425-47 

55 

76.42 

156.66 

241.10 

330.15 

424-35 

56 

76.17 

*56  13 

240.30 

329.07 

423.00 

57 

75-90 

x55-56 

2.39-39 

32783 

42r.53 

58 

75.60 

I54-92 

238.36 

326.42 

419.79 

59 

75,28 

154-23 

237.24 

324-93 

417.92 

60 

74.92 

I53-46 

236.08 

323-35 

4I5-99 

OF  LIFE  INSURANCE. 


87 


TABLE  No.  XXIII— (CONTINUED.) 

NET  VALUE  PER  $  1,000  OF  A  TEN-YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Sixth 
year. 

Seventh 
year. 

Eighth 

year. 

Ninth 
year. 

Tenth 
year. 

20 

537-04 

643.89 

756-45 

875.04 

I,OOO.OO 

21 

536.99 

643.83 

756.40 

875.01 

IjOOO.OO 

22 

53693 

643-77 

756.35 

874.98 

IjOOO.OO 

23 

536.86 

643-7I 

75630 

874-95 

I,OOO.OO 

24 

536-79 

64365 

756.25 

874.92 

I,OOO.OO 

25 

536.72 

643-59 

756.20 

874.88 

1,000.00 

26 

643.52 

756.14 

874.84 

I.OOO.OO 

27 

536-57 

643-44 

756.07 

874.80 

IjOOO.OO 

28 

536-49 

756.00 

874.76 

I,OOO.OO 

29 

536.40 

643.27 

755-92 

874.71 

I.OOO.OO 

30 

536.29 

643-I7 

755-84 

874.66 

1,000.00 

31 

536-I8 

643.06 

755-75 

874.60 

1,000.00 

32 

536.06 

642.94 

755-65 

874-54 

I,OOO.OO 

33 

535-94 

642.82 

755-54 

874.47 

IjOOO.OO 

34 

535-Si 

642.69 

755-42 

874.40 

I,OOO.OO 

35 

535-66 

642.54 

755-29 

874-3I 

I.OOO.OO 

36 

535-49 

642.37 

755-H 

874.21 

I,OOO.OO 

37 

535-31 

642.18 

754-98 

874.10 

IjOOO.OO 

38 

535-" 

641.97 

754.80 

873-99 

1,000.00 

39 

534-90 

641.76 

754-62 

873.87 

I,OOO.OO 

40 

534-69 

64I-55 

754-42 

873-74 

I,OOO.OO 

534-44 

641.30 

754.18 

873-59 

I,OOO.OO 

42 

534-1.5 

641.01 

753-90 

873-4I 

IjOOO.OO 

43 

533-88 

640.67 

753-58 

873.20 

1,000.00 

44 

533-53 

640.31 

753-25 

872.97 

1,000.00 

45 

533-13 

639.90 

752-00 

872.72 

1,000.00 

46 

53^-68 

639.42 

752-46 

872.43 

1,000.00 

47 

532-" 

638.85 

752.03 

872.09 

1,000.00 

48 

531-44 

638-17 

871.68 

1,000.00 

49 

530.77 

6.37-44 

750.70 

871.25 

1,000.00 

50 

529.99 

636.64 

749.98 

870.79 

I,COO.OO 

51 

529.12 

635.72 

749-15 

870.27 

1,000.00 

52 

528.10 

634.66 

748.20 

869.64 

1,000.00 

53 

526.94 

633.46 

747.07 

868.98 

1,  000.00 

54 

525-71 

632^8 

745-94 

868.19 

1,000.00 

55 

524-33 

630.83 

744.81 

867-39 

1,000.00 

56 

522.79 

629.27 

743-44 

866.50 

1,000.00 

57 

520.96 

627.46 

741.82 

865.45 

1,000.00 

58 

518.95 

625.38 

739.96 

864.24 

1,000.00 

59 

516.91 

623.29 

738.o6 

862.98 

1,000.00 

60 

514.86 

621.09 

736-09 

861.64 

1,000.00 

83 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXIV. 


NET  VALUE    PER  $1.000  OF  A  FIFTEEN-YEAR  ENDOWMENT  POLICY, 
AT  THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Aft. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

45-37 

93.10 

143-34 

196.21 

251.86 

310.45 

372.13 

437.08 

21 

45-36 

93.08 

H3-3I 

196.17 

251.82 

310.40 

372-07 

437-02 

22 

45-35 

93.06 

143.28 

196.13 

251.76 

310.34 

372.00 

436.94 

23 

45-34 

93-04 

143.26 

196.10 

25I-72 

310.29 

371-94 

436.87 

24 

45-33 

93-03 

H3-23 

196.06 

251.68 

310.23 

37I-87 

436-79 

25 

45-33 

93-02 

143.20 

196.03 

25I-63 

310.16 

371.80 

436-7I 

26 

45-32 

93.00 

143.18 

J95-99 

25I-58 

310.11 

371-73 

436.62 

27 

45-3i 

92.99 

J43-i5 

195-95 

25I-53 

310.04 

37I-65 

436.53 

28 

45-30 

92-97 

143.12 

I95-92 

251.48 

309.98 

371-57 

436.44 

29 

45-29 

92-95 

143.10 

195.88 

251.42 

309.90 

37I-48 

436.34 

30 

45-29 

92.94 

143.08 

I95-83 

25I-37 

309.84 

37I-40 

436.24 

31 

45-29 

92  '93 

143-05 

195-79 

25I-32 

309-77 

37I-3I 

436.12 

32 

4.;.28 

92.91 

143.02 

I95-76 

251.26 

309.69 

371.2! 

436-00 

33 

45-27 

92.89 

143.00 

I95-72 

261.20 

309.61 

371.10 

435-87 

34 

45-27 

92.89 

142.98 

195.69 

251.14 

309-53 

370-99 

435-74 

35 

45-27 

92.88 

142.96 

I95-65 

251.09 

309.44 

370.88 

435-6o 

36 

45-27 

92.88 

142.94 

195.61 

251.02 

309-35 

370-76 

435-46 

37 

45-27 

92.87 

142.92 

195-57 

250.96 

309.27 

370.66 

435-31 

38 

45-27 

92.87 

142.91 

195-54 

250.91 

309.19 

370-55 

435-17 

39 

45.28 

92.88 

142.92 

195-54 

250.88 

309-I3 

370-45 

435-02 

40 

45-29 

92.89 

142.93 

195-54 

250.87 

309.09 

370.36 

434.89 

4i 

45-32 

92-93 

142.97 

195-57 

250.88 

309-05 

370.28 

434-74 

42 

45-35 

92.98 

143.02 

195.61 

250.89 

309.02 

370.18 

434-56 

43 

45-39 

93-04 

143.09 

195.66 

250.91 

308.98 

370.06 

434-35 

44 

45-43 

93.12 

143.16 

I95-72 

250.92 

308.92 

369.91 

434-09 

45 

45-49 

93-20 

H3-25 

I95-78 

250.92 

308.83 

369.70 

433-77 

46 

45-54 

93.28 

143-33 

195.81 

250.87 

308.68 

369-44 

43338 

47 

45.60 

93-37 

143.40 

195.82 

250.80 

308.50 

369-13 

432-93 

48 

45-66 

93-43 

M3-43 

195-79 

250.67 

308.25 

368.74 

432-39 

49 

45-70 

93-47 

H3-43 

I95-72 

250.50 

307-94 

368.27 

431-75 

5° 

45-74 

93-51 

143.42 

I95-63 

250.28 

307-58 

367-73 

43I-07 

5' 

45-78 

93-54 

i43-4i 

195-52 

250.04 

307.16 

367-13 

430-24 

52 

42.81 

93'  57 

143-37 

I95-3S 

249-75 

306.70 

366.46 

429.34 

53 

45.86 

93-59 

H3-33 

195.22 

249-43 

306.18 

365-72 

428.36 

54 

45-89 

93.61 

143.28 

195.04 

249.08 

305-6I 

364.90 

427.26 

55 

45-93 

93-63 

143.22 

194.85 

248.69 

304.98 

363-99 

426.06 

56 

45-97 

93-65 

143.16 

194.64 

248.27 

304-30 

363.00 

424.76 

57 

46.03 

93-69 

143.10 

194.42 

247.82 

303-56 

361-95 

423-35 

53 

46.09 

93-73 

I43-05 

194.19 

247-34 

302.78 

360.81 

421.81 

59 

46.16 

93-78 

142.98 

193-93 

246.82 

301-93 

359-55 

420.12 

60 

46.23 

93-83 

142.92 

I93-67 

246.28 

301.00 

358.18 

418.27 

OF  LIFE   INSURANCE. 


TABLE  No.  XXIV— (CONTINUED.) 

NET  VALUE  PER  $I,OOOOF  A  FIFTEEN-YEAR  ENDOWMENT  POLICY,  AT 
THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4$-  PER  CENT. 


4g* 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thirteenth 
year. 

Fourteenth 
year. 

Fifteenth 
year. 

20 

505  4S 

577-52 

653-40 

733-35 

817.60 

906.40 

1,000 

21 

505-4I 

577-45 

653-33 

733-28 

81754 

906-36 

1,000 

22 

505-32 

577-36 

653-25 

733-21 

817.48 

906.32 

1.  000 

23 

505-25 

577-28 

653-I6 

733-13 

817.4.2 

906.28 

I.OOO 

24 

505-I7 

577-19 

653-07 

733-05 

817-35 

906.24 

1,000 

25 

505-07 

577-09 

652.88 

732.96 

817.28 

906.20 

1,000 

26 

504.98 

57699 

652.87 

732.86 

817.20 

906.15 

I.OOO 

27 

504.88 

576.88 

6:52.76 

732-76 

817.12 

906.09 

1,000 

28 

504-78 

576.78 

652-65 

732-65 

817.02 

906.03 

1,000 

29 

504.66 

576.64 

652.52 

732-52 

816.92 

905-97 

1,000 

30 

504-54 

576.51 

652.38 

732-39 

816.80 

905.90 

1,000 

31 

504.41 

576-37 

652.24 

732-25 

816.68 

905-83 

1,000 

32 

504.26 

576.21 

652.07 

732.10 

816.55 

905-74 

I.OOO 

33 

504.12 

576.05 

651.90 

73*  -93 

816.41 

905-65 

1,000 

34 

503-96 

575-88 

651.72 

73*  -75 

816.25 

905-55 

1,000 

35 

503.80 

575-69 

65L52 

731-56 

816.08 

905.44 

1,000 

36 

503-63 

575  49 

651-31 

731-34 

81^.89 

905-3I 

1,000 

37 

503-45 

575-29 

651.08 

73«-« 

815.68 

905*17 

1,000 

38 

503.26 

575-07 

650.84 

730-85 

8*5-45 

905.02 

1,000 

39 

503-07 

574-83 

650.56 

730-56 

815.19 

904.84 

1,000 

40 

502.88 

574-58 

650.26 

73024 

814.89 

904.65 

1,000 

4i 

502.66 

574-29 

649.91 

72987 

814  16 

904.43 

I.OCO 

42 

502.40 

573-94 

649.51 

729.46 

814.18 

904.  18 

1,000 

43 

502,09 

573-55 

649.06 

72898 

813-76 

903.89 

I/JOO 

44 

501.72 

573-09 

648-53 

728.44 

813.27 

9°357 

1,000 

45 

501.29 

572-55 

647-93 

727.82 

812.72 

903.21 

1,000 

46 

500.77 

5/i  93 

647.23 

727.11 

812.01} 

902  So 

1,000 

47 

500.  i  S 

571.22 

646.44 

726.30 

811.38 

902.34 

1,000 

48 

499.49 

570.40 

64S-54 

72S  39 

Sio.sS 

901.82 

1,000 

49 

498.70 

569-47 

644.52 

724-37 

809.68 

901.23 

1,000 

50 

497.84 

568.47 

643-38 

723-23 

808.68 

900.58 

1,000 

5i 

490-.  8  1 

567-27 

642.11 

721-95 

807.56 

899.86 

I.OOO 

52 

49v7o 

565-97 

640.69 

720.54 

806.32 

899.05 

I.OOO 

'53 

494.48 

564-54 

639-13 

718.97 

804-93 

898.14 

1,000 

54 

493-^2 

562.96 

637.42 

7'7-23 

803.40 

897.14 

I.OOO 

55 

491.63 

561-23 

635-5I 

715  31 

801.72 

896.03 

1,000 

56 

490.01 

560.32 

633-4' 

7T3  20 

79983 

894.79 

1,000 

57 

488.24 

557-24 

631-13 

7IO.S6 

797-75 

893.42 

1,000 

<8 

486.31 

5  5*  -06 

628.58 

708.28 

7<J5  44 

891.88 

1,000 

59 

484.18 

552-43 

625-79 

705.42 

792.89 

890.  20 

1,000 

60 

481-83 

549-64 

622.68 

702.24 

790.05 

888.34 

1,000 

£0  PRINCIPLES  AND  PRACTICE 

TABLE   No.  XXV. 

NET  VALUE  PER  $1,000,  OF  A  TWENTY- YEAR  ENDOWMENT  POLICY,  AT 
THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4  PER  CENT 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

29-45 

60.41 

92.98 

127.23 

163.27 

2OI.2O 

241.10 

283.10 

21 

29.44 

60.40 

92.97 

127.22 

163.26 

201.  IS 

241.07 

283.06 

22 

29.44 

60  40 

92.96 

127.22 

163-25 

201.16 

241.06 

283.03 

23 

29.44 

60.40 

92.97 

127.22 

163.25 

201.16 

241.04 

283.01 

24 

29.44 

60.41 

92.97 

127.22 

163-25 

201.15 

241.02 

282.99 

25 

29-4> 

60.42 

92.98 

127.23 

163.26 

2OI.I5 

241.02 

282.98 

26 

29-45 

60.42 

92.99 

127.24 

163.26 

2OI.I5 

241.01 

282.95 

27 

29.46 

60.44 

93.01 

127.25 

163.27 

201.16 

241.01 

282.94 

28 

29.47 

60.45 

93.02 

127,28 

163.30 

201.17 

241.02 

282.94 

29 

29.48 

60.47 

93-05 

127.31 

163-32 

201.20 

241.04 

282.95 

30 

29.50 

60.50 

93-09 

127-34 

163-36 

2OI.24 

241.07 

282.96 

31 

29.52 

60.54 

93-13 

127-39 

163.42 

2OI.29 

241.12 

283.00 

32 

29-54 

60.57 

93.18 

127.46 

163.48 

201.36 

241.17 

283.04 

33 

29.56 

60.61 

93-25 

127-53 

163.57 

201-43 

241.24 

283.10 

34 

29-59 

60.68 

93-33 

127.64 

163.68 

201-55 

24I-35 

283.20 

35 

29.64 

60.76 

93-44 

127.76 

163.81 

201.68 

241.49 

283.33 

36 

39.68 

60.84 

93-55 

127.90 

163.96 

201.85 

241.65 

283.49 

37 

29.74 

60.94 

93-69 

128.06 

164.15 

202.06 

241.87 

283.69 

33 

29.79 

61.05 

93-84 

128.26 

164.39 

202.32 

242.14 

283.96 

39 

29.87 

61.19 

94-05 

128.52 

164.69 

202.64 

242.47 

284.27 

40 

29-95 

61.36 

94.29 

128.82 

165-03 

203.01 

242.84 

284.64 

4i 

30.06 

61.^6 

94-58 

129.17 

165.44 

203.44 

243.29 

285.06 

42 

30.18 

61.80 

94.90 

129.58 

165.89 

203.93 

243-77 

285-50 

43 

30-33 

62.06 

95.28 

130.03 

166.41 

204.47 

244.29 

285.96 

44 

30.48 

62.36 

95-69 

I30.54 

166.97 

205.04 

244.83 

286.45 

45 

30.66 

62.69 

96.15 

131.09 

167.56 

205.63 

245.40 

286.95 

46 

30-85 

63.04 

96.63 

I3I-65 

168.16 

206.24 

245-97 

287.45 

47 

31.06 

63-43 

97.14 

I32-25 

168.80 

206.88 

246.57 

287.97 

48 

31.29 

63-83 

97-67 

I32.86 

169.46 

207-54 

247.18 

288.50 

49 

Si-Si 

64.23 

98.21 

133-49 

170.15 

208.23 

247.83 

289.04 

50 

31-74 

64.66 

9S-79 

134.18 

170.88 

208.96 

248.51 

289.62 

5i 

32.00 

65.12 

99.41 

I34-91 

171.67 

209.75 

249.24 

290.25 

52 

32.27 

65-63 

100.09 

I35-71 

172.52 

210.61 

250.05 

290.94 

53 

32-58 

66.17 

100.83 

I36-57 

173-45 

2H-55 

250  93 

291.69 

54 

32.89 

66.76 

101.62 

'37-50 

174-47 

212.58 

251.89 

292.51 

55 

33-25 

67.40 

102.48 

138-53 

175-59 

213.70 

252.94 

293-4I 

56 

33-62 

68.09 

103.42 

J39-65 

176.79 

214.91 

254.08 

294-39 

57 

34-03 

68.84 

104.44 

140.85 

178.09 

216.22 

255-31 

295.46 

58 

34.48 

69.66 

105-54 

142.14 

179-48 

217.63 

256.64 

296.58 

59 

34-95 

70.52 

106.70 

H3-5I 

180.97 

219.13 

258-03 

297-75 

60 

35-45 

71.44 

107.94 

144.98 

182.57 

220.71 

259.48 

298.96 

OF  LIFE  INSURANCE. 


TABLE  No.  XXV— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TWENTY- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Affe. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

T-uielfth 
year. 

ThirPnth 
year. 

Fourteenth 
year. 

Fifteenth 
year. 

20 

327.29 

373-82 

422.80 

474-37 

528.68 

-Or  CO 
505.0O 

646.14 

21 

327.24 

373-75 

422.74 

474-30 

528.60 

585-79 

646.05 

22 

327.21 

373-72 

422.68 

474-23 

528.52 

585-70 

645.96 

23 

327.18 

373-67 

422.62 

474.16 

528.44 

585-6I 

645.86 

24 

327-I5 

373-63 

422.56 

474.09 

528.35 

585.52 

645-76 

25 

327.12 

373-59 

422.51 

474.02 

528.27 

585-42 

645-65 

26 

327.08 

373-54 

422.45 

473-95 

528.18 

585-32 

645-53 

27 

327-07 

373-51 

422.40 

473.S7 

528.09 

585.20 

645.41 

28 

327-05 

373-48 

422.35 

473.80 

527.99 

585." 

645.28 

29 

327-05 

373-45 

422.29 

473-72 

527.89 

5S4-97 

645.14 

3° 

327-03 

373-42 

422.25 

473-65 

527.80 

584-86 

645.01 

31 

327.06 

373-42 

422.22 

473-59 

527-72 

584.74 

644.86 

32 

327.08 

373-42 

422.19 

473-54 

527-63 

584.63 

644.72 

33 

327.12 

373-44 

422.19 

473-51 

527-56 

584.52 

644.58 

34 

327.20 

373-50 

422.22 

473-50 

527-5I 

584.42 

644-43 

35 

327-32 

373-59 

422.27 

473-50 

527.46 

584-32 

644.27 

36 

327-47 

373-71 

422.34 

473-53 

527.42 

584.20 

644.09 

37 

327-65 

373-85 

422.45 

473-57 

527-39 

584.09 

643.88 

38 

327-88 

374-05 

422.58 

473.62 

527-34 

583-94 

643-65 

39 

328.17 

374-29 

422.73 

473-67 

527-29 

583-78 

643.40 

40 

328-50 

374-54 

422.89 

473-72 

527.21 

583-59 

643.  10 

4i 

328.86 

374-Si 

423.05 

473-76 

527-I3 

583-37 

642.75 

42 

329.23 

375-o8 

423.21 

473-79 

527-00 

5S3-IO 

642.35 

43 

329.61 

375-35 

423.36 

473-78 

526.84 

582.78 

641.89 

44 

330.01 

375-64 

423.49 

473-75 

526.63 

582.40 

64L35 

45 

330-4* 

375-91 

423.60 

473-68 

526.37 

581.95 

640.74 

46 

330.80 

376.15 

423-67 

473-56 

527-05 

581.43 

640.04 

47 

331-20 

376.39 

423.73 

473-40 

525-67 

580.83 

639^3 

48 

33!-6o 

376-62 

423.75 

473-20 

525-22 

580.14 

638.33 

49 

332.00 

376.84 

42376 

472-95 

524-71 

579-36 

637.32 

50 

332-43 

377.08 

433.74 

472.67 

524.I3 

578.50 

636.20 

5i 

332-89 

377-32 

423.73 

472-35 

523.52 

577-56 

634-97 

52 

333-40 

377-59 

423.7I 

472.02 

522.83 

576.53 

633.62 

53 

333-95 

377-89 

423.74 

471.67 

522.21 

575-41 

632.15 

54 

334-57 

378.24 

423.72 

471.29 

521.40 

574'lS 

630.52 

55 

335-25 

378.63 

423-74 

470.88 

520.42 

572.82 

628.72 

56 

335-99 

379-03 

423-74 

470.41 

519.42 

571.30 

626.70 

57 

336.78 

379-46 

423.72 

469.85 

518.29 

569.57 

624.43 

58 

337-6o 

379-87 

423.62 

469.17 

516.97 

567.60 

621.88 

59 

338.43 

380.24 

423-43 

468-34 

5I5.43 

565.39 

619.09 

60 

339-26 

380.57 

423-I3 

467-34 

5I3-7I 

563.00 

616.13 

9a  PRINCIPLES  AND  PRACTICE 

TABLE  No.  XXVI. 

NET  VALUE  PER  $1,000.  OF  A  TWENTY-FIVE  YEAR  ENDOWMENT  POLICY, 
AT  THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

20.36 

4*-75 

64.24 

87-87 

112.72 

138-85 

166.33 

195.22 

21 

20.37 

41-77 

64.26 

87-QO 

112.76 

138.89 

166.37 

195.27 

22 

20.37 

41.78 

64.29 

87.94 

112.  8l 

138.95 

166.43 

I95-32 

23 

20.39 

41.81 

64-33 

87.99 

112.86 

139.01 

166.49 

195-39 

24 

20.41 

41.85 

64.38 

88.05 

112.94 

139.09 

166.58 

195.48 

25 

20.43 

41.89 

64-43 

88.13 

113.02 

139.18 

166.68 

195-59 

26 

20.45 

41-93 

64.50 

88.21 

113.12 

I39-30 

166.81 

I95-7I 

27 

20.48 

41.99 

64.58 

88.31 

113.24 

139-43 

166.95 

I95-87 

28 

20.51 

42.05 

64.67 

88.43 

"3-38 

!39-59 

167.12 

196.06 

29 

20-55 

42.12 

64.78 

88.57 

"3-54 

139-77 

167.33 

196.28 

30 

20.59 

42.21 

64.91 

88.73 

"3-74 

140.01 

167.58 

I96-55 

31 

20.65 

42-32 

65-05 

88.91 

ii3-97 

140.27 

167.88 

196.86 

32 

20.71 

42.43 

65.22 

89.14 

114.23 

M0.57 

168.21 

197.22 

33 

20.77 

42.56 

65.42 

89-39 

"4-55 

140.93 

168.61 

197.64 

34 

20.85 

42-73 

65-65 

89.70 

114.91 

i4!-35 

169.07 

198.15 

35 

20.95 

42.91 

65-93 

90.05 

"5-33 

141.83 

169.61 

198.74 

36 

21.06 

43.12 

66.23 

90.44 

115.80 

142.38 

170.23 

199.42 

37 

21.  l8 

43-36 

66.  s  8 

90.89 

116.36 

H3-03 

170.96 

2OO.22 

38 

21.31 

43.62 

66.97 

91.41 

116.99 

J43-77 

171.79 

2OI.I2 

39 

21.47 

43-93 

67-43 

92.01 

"7-73 

144.62 

172.74 

202.15 

40 

21.65 

44.29 

67-95 

92.70 

118.56 

H5-58 

173.81 

203.30 

4i 

21.86 

44.70 

68.56 

93-48 

119.51 

146.67 

175.02 

204.59 

42 

22.09 

45.16 

69.23 

94-36 

I2o-55 

147.87 

176-34 

205.99 

43 

22.36 

45.68 

69-99 

95-33 

121.72 

149.20 

177.78 

207.50 

44 

22.65 

46.25 

70.82 

96-39 

122.99 

150.62 

I79-3I 

2O9.II 

45 

22.98 

46.88 

7i-73 

97-55 

124-35 

152.15 

180.97 

210.85 

46 

23-32 

47-56 

72.71 

98-79 

1215.80 

153-77 

182.73 

212.17 

47 

23-71 

48.30 

73-76 

IOO.  IO 

127-35 

I55-5I 

184.62 

214.69 

48 

24.12 

49.08 

74.87 

101.50 

129.00 

157-37 

186.63 

216.82 

49 

24-55 

49.89 

76.03 

102.98 

U0.75 

159-35 

188.79 

212.08 

50 

25.00 

50-77 

77-29 

104.58 

132.64 

161.48 

191.10 

221-53 

5i 

25-49 

5J-7i 

78.64 

106.30 

I34-67 

163.76 

193-59 

224.17 

52 

26.02 

52-72 

80.09 

108.14 

I34-85 

166.22 

196.27 

227.OO 

53 

26.  sS 

53-So 

81.65 

IIO.  1  1 

139.18 

168.86 

199.14 

230.03 

54 

27.18 

54-95 

83-30 

112.  21 

141.67 

171.67 

202.20 

233-25 

55 

27.82 

56.18 

85.06 

114.46 

H4-33 

174.67 

205.46 

236.69 

56 

28.50 

57-49 

86.95 

116.85 

147.16 

I77-S5 

208.92 

240.35 

57 

29.23 

58.89 

88.96 

"9-39 

150.14 

iSz.23 

212.60 

244.24 

58 

30.01 

60.38 

91.09 

122.19 

153-34 

184.82 

216.50 

248.34 

59 

30.82 

61.95 

93-33 

124.92 

156.70 

188.61 

220.60 

252.64 

60 

31.68 

63-59 

95-69 

127.92 

160.25 

192.59 

224.91 

257.I7 

OF  LIFE   INSURANCE. 


93 


TABLE  No.  XXVI— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TWENTY-FIVE  YEAR  ENDOWMENT  POLICY, 
AT  THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Ninth 
year. 

Tenth 
year. 

Eleventl 
year. 

T-velfth 
year. 

ThirPnt 
year. 

Four'ntl 
year. 

Fifteent) 
year. 

;  Twenfth 
year. 

20 

225.61 

257-57 

291.20 

326.57 

363-79 

402.96 

444.19 

685-59 

21 

225-65 

257.61 

291.23 

326.60 

363-80 

402.96 

444.18 

685.50 

22 

225.71 

257.66 

2QI.28 

326.63 

363-83 

402.98 

444.18 

685.41 

23 

225-77 

257-73 

291  -33 

326.68 

363-87 

403.01 

444.20 

685-31 

24 

225.87 

257.81 

291.41 

326.75 

363-93 

403-05 

444-21 

685.22 

25 

225.97 

257-91 

291.51 

326.84 

364.01 

403.10 

444.24 

685.13 

26 

226.IO 

258-05 

291.64 

326.96 

364.10 

403.18 

444.29 

6^5.04 

27 

226.26 

258.21 

291.79 

327.10 

364-23 

403.28 

444-37 

684.95 

28 

226.46 

258.41 

291.98 

327-27 

364-38 

403.42 

444-48 

684.87 

29 

226.69 

258.64 

292.21 

327-49 

364.59 

403-59 

444-63 

684.80 

30 

226.97 

258.92 

292.48 

327-75 

364.84 

403-83 

444-S3 

684-73 

31 

227.29 

259.24 

292.81 

328.08 

365-I5 

404.  1  1 

445.08 

684.65 

32 

227.66 

259-63 

293.21 

328.48 

365-53 

404.46 

445-37 

684.57 

33 

228.12 

260.  10 

293-69 

328.95 

365-98 

404.88 

445-75 

684.47 

34 

228.65 

260.67 

294.26 

329-52 

366-52 

405-37 

446.19 

684.37 

35 

229.29 

261.32 

294.93 

330.17 

367-I4 

405-94 

446.67 

684.26 

36 

230.01 

262.08 

295.68 

330.91 

367-85 

406.58 

447.22 

684.12 

37 

230.86 

262.95 

296.56 

33I-76 

368.64 

407.28 

447-78 

683.96 

38 

231.82 

263.94 

297-54 

332-70 

369-50 

408.04 

448-44 

683.78 

39 

232.89 

265.04 

298.63 

333-74 

370-45 

408.88 

449.14 

683.58 

40 

234.10 

266.21; 

299.81 

334-86 

371-49 

409-79 

449-89 

683-33 

4i 

235-43 

267.58 

301.10 

336-08 

372.61 

410.77 

450.70 

683.05 

42 

236.86 

269.01 

302.49 

337-40 

373-Si 

411.83 

45I-58 

682.73 

43 

238.40 

270.55 

3°3-99 

338.82 

375-10 

412.95 

452.49 

682.35 

44 

240.07 

272.21 

305.60 

340-33 

376.48 

4H-I5 

453-48 

681.92 

45 

241.84 

273.98 

307-32 

341-95 

377-95 

4I5-44 

454-53 

681.44 

46 

243-74 

275-87 

309.16 

343-68 

379-53 

416.81 

455-65 

680.89 

47 

245-77 

277.90 

311.14 

345-55 

381-23 

418.29 

456-85 

680.28 

48 

247-95 

280.07 

313-26 

347-56 

383.06 

419.87 

458-14 

679.60 

49 

250.28 

282.42 

3I5-53 

349-  y° 

385-01 

421-57 

459-53 

678.83 

50 

252.80 

284.94 

318.00 

352-03 

387-13 

423.42 

461.04 

677-97 

5i 

255-5I 

287.64 

320.64 

354-53 

389.42 

425.42 

462.66 

676.97 

52 

258.42 

290.57 

323-48 

357-22 

391.88 

427-54 

464-38 

675.82 

53 

26l.53 

293.68 

326.52 

360.10 

394-48 

429-79 

466.18 

674-5I 

54 

264.85 

297.00 

329-76 

363-14 

397-24 

432.16 

468.04 

673.06 

55 

268.38 

300.55 

333-19 

366.36 

400.14 

434.62 

469.97 

67I-53 

56 

272.14 

304.29 

336-81 

369-75 

403-17 

437-i8 

471.94 

670.00 

57 

276.28 

308.24 

340-63 

373-31 

406.35 

439-85 

473-98 

668.60 

58 

280.31 

312.41 

344.64 

377-05 

409.67 

442.64 

476.  19 

667-44 

59 

284.71 

316.77 

348-85 

380.95 

413.16 

445-66 

478.69 

666.62 

60 

289.31 

321-34 

353-24 

395-05 

416.91 

449.03 

481.66 

666.25 

94  PRINCIPLES  AND  PRACTICE 

TABLE  No.  XXVII. 

NET  VALUE  PER  $1,000  OF  A  THIRTY- YEAR  ENDOWMENT,  AT  THE  END 
OF  VARIOUS  YE\RS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

rft-f/ 

year. 

Second 
\ear. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eiffhtli 
year. 

20 

14.69 

30.11 

46.30 

63-30 

8l.I7 

99-94 

119.66 

140.38 

21 

17.71 

30.15 

46-36 

63-39 

81.28 

100.07 

119.80 

HO-  54 

22 

14-73 

30.20 

46.44 

63.50 

81.41 

IOO.22 

119.98 

H0-  73 

23 

14.76 

30.26 

46-54 

63.62 

81.56 

100.40 

120.18 

MO-  95 

24 

14.80 

30-34 

46.65 

63-77 

81.74 

100.61 

120.42 

141.22 

25 

14.85 

30-43 

46.78 

63-94 

81.94 

100.85 

120.70 

HtoS 

26 

14.89 

3°-52 

46.92 

64.12 

82.18 

101.13 

121.  01 

141.88 

27 

H-95 

30.63 

470S 

64-34 

82.45 

101.45 

121.38 

142.27 

28 

15.02 

30.76 

47.28 

64.60 

82.77 

101.82 

121.  80 

142.77 

29 

15.09 

30.91 

47-50 

64.89 

83.12 

102.24 

122.30 

H3-32 

30 

I5-I7 

31.08 

47-75 

65.22 

83-54 

102.74 

122.86 

143.96 

31 

15.28 

31.28 

48.04 

65.61 

84.02 

103.31 

I23-52 

144.68 

32 

15-39 

31-49 

48-37 

66.05 

84-56 

103.95 

124.24 

I45-50 

33 

I5-50 

31-74 

48.74 

66.54 

8S-I7 

104.67 

125.08 

146.44 

34 

15-65 

32.03 

49.18 

67.11 

85.88 

105.51 

I26.O4 

*47-52 

35 

15.82 

32-36 

49.66 

67-75 

86.67 

106.44 

127.12 

148-73 

36 

16.00 

32.72 

50.20 

68-47 

87-55 

107.50 

128.33 

150.11 

37 

16.21 

33-13 

50.81 

69.27 

88-55 

108.69 

129.72 

151.65 

38 

16.43 

33-58 

51.48 

70.17 

89.68 

110.03 

131.26 

J53-39 

39 

16.69 

34-09 

52.26 

71.20 

90-95 

111.54 

I32.99 

J55-33 

40 

16.97 

34-67 

53-12 

72-35 

92-37 

113-23 

134.92 

157.48 

4i 

I7-30 

35-32 

54.10 

73.63 

93-97 

115.10 

I37-05 

159.84 

42 

17.66 

36-05 

55-17 

75-05 

95-71 

117-15 

139.28 

162.41 

43 

18.06 

36.84 

56.35 

76.61 

97.62 

119.38 

141.90 

165.17 

44 

18.50 

37-71 

57-64 

78.30 

99.68 

121.79 

144.60 

168.14 

45 

18.99 

38.66 

59-05 

80.14 

101.91 

124.36 

I47-50 

'  I7I-32 

46 

19.50 

39-69 

60.52 

82.09 

104.26 

127.10 

150.58 

174.71 

47 

20.06 

40.69 

62.15 

84.15 

106.77 

130.01 

153-86 

178.31 

48 

20.66 

41.94 

63-83 

86.33 

109.42 

133-09 

157-33 

182.13 

49 

21.27 

43-^3 

65.60 

88.63 

112.22 

136.35 

161.01 

186.17 

50 

21.93 

44-43 

67.48 

91.08 

115.19 

139.81 

164.90 

190.46 

5i 

22.62 

45-79 

69.49 

93-67 

"8.35 

143-47 

169.03 

195.01 

52 

23-36 

47-23 

7i-59 

96.42 

121.68 

147-35 

I73-40 

199.81 

53 

24-I5 

48.78 

73-83 

99-33 

125.21 

151.45 

178.03 

204.89 

54 

24-95 

50-35 

76.17 

102.36 

128.90 

155.75 

182.86 

210.20 

55 

25.82 

52.05 

78.64 

105.58 

132.81 

160.28 

: 

187.96 

215-79 

OF  LIFE   INSURANCE. 


95 


4,  TABLE  No.  XXVII— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  THIRTY- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YKARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thirfnth 
year. 

Fourfnth 
year. 

Fifteenth 
year. 

Twentieth 
year. 

20 

162.15 

185.02 

209.05 

234-32 

260.88 

288.80 

3I8.I5 

489.36 

21 

162.32 

185.20 

209.25 

234-53 

2bi.o8 

28Q.OO 

318.36 

489.46 

22 

162.53 

185.43 

209.49 

234-77 

261.33 

289.25 

318.60 

489.60 

23 

162.77 

185.69 

209.76 

235.05 

261.63 

289-55 

318.89 

489.79 

24 

163.06 

l86.00 

210.09 

235-39 

261.97 

289.90 

3!9-23 

490.03 

2.5 

163.40 

186.36 

210.47 

235-79 

262.38 

290.31 

3^9-64 

490.32 

26 

163.78 

186.78 

210.91 

236.26 

262.85 

290.79 

320.1' 

490.68 

27 

164.24 

187.27 

211.44 

236.79 

263.41 

29I-33 

520.68 

491.  II 

28 

164.76 

187-83 

212.03 

237-42 

264.05 

292.0" 

.**I-3!) 

49^63 

29 

165.37 

188.48 

212.72 

238.14 

264.80 

292.73 

322.13 

492.22 

30 

166.06 

189.23 

213-53 

238.98 

265.68 

293.68 

323-03 

492.90 

31 

166.86 

190.09 

214.44 

239-95 

266.69 

294.71 

324.08 

493.66 

32 

167.76 

191.07 

2I5-51 

241.07 

267.84 

295.90 

32^.27 

494.48 

33 

168.79 

192.20 

216.70 

242.31 

269.17 

297.24 

326.62 

405.42 

34 

169.99 

193-49 

218.07 

243-78 

270.66 

298.77 

328.15 

496.45 

35 

I7I-33 

194-95 

219.63 

24^.42 

272.35 

300.48 

329.84 

497-57 

36 

172-85 

196.60 

221-37 

247.24 

274.23 

302.36 

33I-7'J 

498.79 

37 

174-55 

198.43 

223.33 

249.28 

276.30 

304-43 

333-73 

500.14 

38 

176.45 

200.48 

225.49 

25I-5I 

278.56 

306.70 

335-96 

501-59 

39 

178.57 

202.75 

227.87 

254.00 

281.05 

3oq,i8 

338.40 

503-19 

40 

180.93 

205.25 

230.46 

256.62 

283.75 

311.87 

341.04 

504.92 

4* 

183.47 

207.94 

233-28 

259-52 

286.68 

314.80 

3*3-9i 

506.80 

42 

186.23 

210.87 

236.33 

262.65 

289.85 

3I7-95 

347-01 

508.83 

43 

189.21 

215.02 

239.62 

266.03 

293.26 

32136 

350-35 

511.03 

44 

192.40 

217.40 

243.14 

269.65 

296-93 

325-01 

353-05 

513-41 

45 

195.84 

221.04 

246.93 

273-53 

300.84 

328.04 

3  7-81 

5I5.97 

46 

199.48 

224.89 

250.95 

277.67 

305.06 

333-  '3 

361.92 

518.68 

47 

203.36 

229.00 

255-24 

282.09 

309-53 

337-6° 

366.31 

521.56 

48 

207.48 

233-37 

259.80 

286.77 

314.28 

342.3;5 

370-96 

524.59 

49 

212.84 

237-99 

264.63 

29I-73 

3I9-30 

347-35 

375-90 

527-74 

50 

216.47 

242.90 

269.74 

296.98 

324.62 

352-66 

381.12 

531-01 

5i 

221.36 

248.09 

275-15 

302.54 

330.25 

358-28 

386.62 

534-43 

52 

226.54 

253  55 

280.86 

308.42 

336.20 

364.20 

392.4i 

537-99 

53 

232.01 

259-35 

286.89 

314.60 

342-45 

370.42 

398-50 

54178 

54 

237-72 

265.40 

293.20 

321.07 

348.98 

376.92 

404.84 

545-8y 

55 

243-75 

271.78 

299.82 

327-85 

355-82 

383-70 

411.47 

550.50 

96 


PRINCIPLES  AND  PRACTICE 


TABLE   No.  XXVIII.  % 

NET  VALUE  PER  $1,000  OF  A  THIRTY-FIVE  YEAR  ENDOWMENT  POLICY,  AT 
THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  47  PER  CENT. 


Agt. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

10.97 

22.48 

34-55 

47.21 

60.50 

74-45 

89.08 

104.44 

21 

1  1.  01 

22.56 

34-67 

47-38 

60.72 

74.71 

89.3S 

104.79 

22 

II.  06 

22.65 

34.82 

47-58 

60.96 

75-oo 

89-73 

105.18 

23 

n.  ii 

22-77 

34-99 

47.81 

61.23 

75-34 

90.12 

105.63 

24 

n.  18 

22.90 

35-  J9 

48.07 

61.58 

75-73 

90-59 

106.16 

25 

11.26 

23-05 

35-4i 

48.37 

61.95 

76.18 

91.11 

106.75 

26 

"•34 

23.21 

35-66 

48.70 

62.37 

76.69 

91.69 

107.41 

27 

"•43 

23.41 

35-95 

49.08 

62.85 

77.27 

92.36 

108.18 

28 

"•54 

23.62 

36.27 

49-52 

63-39 

77.91 

93.12 

109.05 

29 

11.66 

23.86 

36.64 

50.01 

64.00 

78.65 

93-99 

110.03 

30 

11.79 

24.14 

37-05 

50.56 

64.70 

79-49 

94-97 

111.15 

31 

"•95 

24-45 

37-52 

5I-I9 

65-49 

80.44 

96.07 

112.40 

32 

12.12 

24.79 

38.04 

51.89 

66.36 

81.49 

97.29 

113.80 

33 

12-31 

25.18 

38-63 

52.68 

67-35 

82.67 

98.67 

"5-37 

34 

12-53 

25.62 

39-29 

53-56 

68.45 

84.00 

IOO.2I 

"7-J3 

35 

12.78 

26.11 

40.03 

54-54 

69.68 

85-47 

101-93 

119.10 

36 

13.04 

26.65 

40.83 

55-62 

71.04 

87.11 

I03-85 

121.29 

37 

13-34 

27.24 

41.74 

56-83 

72.56 

88.93 

105.99 

123.72 

38 

13.66 

27.90 

42-73 

58-17 

74-23 

90.96 

108.34 

126.41 

39 

14.03 

28.63 

43-84 

59-65 

76.11 

93-20 

110-95 

129.36 

40 

14-43 

29-44 

45.06 

61.29 

78.15 

95-65 

"3-79 

132.58 

4i 

14.88 

30-34 

46.42 

63.09 

80.41 

98.33 

116.90 

136.06 

42 

I5-36 

3I-32 

47-88 

65.06 

82.84 

101.24 

120.21; 

139.84 

43 

15.90 

32-39 

49.48 

67.17 

85-47 

104.36 

123-83 

143-85 

44 

16.47 

33-54 

51.20 

69-45 

88.29 

107.68 

127.63 

148.10 

45 

17.10 

34-78 

53-°4 

71.88 

91.28 

in.  20 

131-65 

152.60 

46 

17-75 

36.09 

54-99 

74-44 

94.42 

114-90 

135-88 

157-34 

47 

18.46 

37-49 

57-05 

77-H 

97.72 

118.80 

140.34 

162  32 

48 

I9.2O 

38-94 

59-  *  9 

79-95 

101.17 

122.88 

149.88 

167  54 

49 

19.96 

40.44 

61.42 

82.88 

104.81 

127.14 

145.00 

172.98 

50 

20.76 

42.03 

63-77 

85-97 

108.59 

131.61 

154.98 

178.69 

OF  LIFE  INSURANCE. 


97 


TABLE  No.  XXVIII.— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  THIRTY-FIVE  YEAR  ENDOWMENT  POLICY,  AT 
THE  END  OF  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thir- 
teenth 
year. 

Four- 
teenth 
year. 

Fifteenth 
year. 

Twentieth 
year. 

2O 

120-57 

137-49 

I55-25 

173-88 

193.46 

214.01 

235-58 

360-80 

21 

120.95 

I.37-91 

I55-70 

I74-38 

193.98 

214-55 

236.15 

361.39 

22 

121.39 

138.40 

156.23 

174.96 

I94-58 

215.19 

239.81 

262.09 

23 

121.89 

I3S95 

156-83 

175-59 

I9.v27 

215.92 

237.58 

362-91 

24 

122.48 

U9-59 

I57-52 

I/6-34 

196.07 

216.76 

238.45 

363-87 

25 

123.14 

140.32 

158.32 

177.20 

196.99 

217.72 

239.46 

36497 

26 

123.88 

141.14 

I59-23 

178.18 

igS.02 

218-82 

240.60 

366  23 

27 

^4-75 

142.09 

160.26 

179.28 

199.21 

22O.O6 

241,91 

2G/.67 

28 

125.72 

I43-I7 

'161.43 

180.55 

200.55 

221.49 

24342 

3693' 

29 

126.82 

I44-38 

162.75 

181.97 

202.08 

223.11 

245.11 

37I-I5 

30 

128.07 

I45-76 

164.25 

183-59 

203.80 

224.94 

247-03 

37320 

31 

129.47 

I47-30 

165.94 

185.41 

205.75 

227.0: 

249  2O 

375-46 

32 

1.3  «  -03 

149.04 

167.84 

187.47 

207.95 

229.33 

251.63 

377-95 

33 

132.80 

15099 

169.97 

189.77 

210.41 

231.92 

254-33 

380.69 

34 

I34-7S 

153-lS 

172.36 

i92-35 

2I3-I5 

234.81 

257.32 

383-69 

35 

136.99 

i  55-6  1 

175.02 

195.20 

216.19 

237-99 

260.62' 

386.96 

36 

'3943 

158.32 

177.96 

198-35 

219.  S2 

241.47 

264.21 

390.52 

37 

142.16 

161.32 

lSl.20 

201.83 

223.18 

245-27 

268.12 

394-39 

33 

145-15 

164.60 

184.76 

205.60 

227.15 

249.40 

272.36 

398.58 

39 

I48-45 

16^.21 

lSS.62 

209.70 

23I-45 

253.86 

276.96 

403.11 

40 

1152.02 

172.09 

192.79 

214.12 

236.08 

258.68 

281.90 

407.99 

4i 

155  89 

176.28 

197.28 

218.87 

241  06 

263  84 

287.21 

4t3  23 

42 

160.02 

180.76 

202.08 

223-95 

246.38 

269.35 

292.87 

418.81 

43 

164.42 

185-54 

207.19 

229.36 

2S2.04 

275.22 

298.89 

424-73 

44 

169.  10 

190.60 

2I2.6O 

235.08 

258.02 

281.42 

305-27 

431.00 

45 

174-05 

195.96 

218.33 

241.13 

264-35 

287.99 

312.00 

437-61 

46 

17925 

201.59 

224-34 

247.49 

271.OI 

294.88 

319.08 

444-54 

47 

184.70 

207.5; 

230.67 

254.  18 

2/S.OI 

302.13 

326.49 

451-79 

48 

190.45 

213.71 

237,30 

261.19 

2S.S-33 

30971 

334-28 

-159-36 

49 

196.43 

220.20 

244-23 

268.50 

292.97. 

317.61 

342-39 

467.22 

50 

202.71 

226.98 

25I-47 

276.14 

300.95 

325-87 

350.85 

475-38 

COMBINED   EXPERIENCE   TABLE   OF 
MORTALITY. 

This  table  of  mortality,  which  was  the  result  of  the  united 
efforts  of  the  actuaries  of  seventeen  life  offices  of  England  and 
Scotland,  and  for  this  reason  is  often  termed  the  "  Actuaries " 
table,  is  a  far  better  criterion  of  mortality  than  any  which  pre- 
ceded it.  Heretofore,  all  tables  of  mortality  were  made  from 
the  average  population  of  certain  towns  or  countries,  which 
included  large  numbers  of  persons  who  were  not  proper  sub- 
jects for  insurance,  and  consequently,  the  mortality  record  was 
much  greater  than  was  needed  for  the  successful  determination 
of  the  mortality  of  insured  lives.  But  in  this  case,  none  but 
selected  and  insured  lives  were  taken.  It  comprises  the  recorded 
experience  of  the  Amicable,  Alliance,  British  Commercial, 
Crown,  Economic,  Eqetitablc,  Guardian,  Imperial,  Law 
Life,  London  Life,  Norwich  Union,  Promoter,  Scottish 
Widows'  Fund,  Sun,  Universal,  and  University  offices.  The 
data  of  these  offices  was  collected  under  the  superintendence  of 
a  committee  of  actuaries,  who  availed  themselves  of  all  the 
experience  and  research  of  those  who  had  preceded  them,  in 
order  to  get  a  reliable  table  to  measure  the  average  mortality  of 
assured  lives.  It  was  first  published  by  Jenkin  Jones,  in  1843, 
and  from  that  time  till  the  present,  it  has  been  highly  appreci- 
ated by  the  actuaries  of  England  and  America.  The  statistics 
upon  which  this  table  was  founded  have  never  yet  been  made 
public,  only  a  few  copies  of  them  were  printed,  and  they  only 
for  private  circulation. 

An  objection  has  been  raised  against  this  table,  that  the  aver- 
age age  of  the  policies  was  only  8^  years,  and  that  for  lives 
which  continue  long  in  the  company,  this  table  would  be  found 
defective.  The  experience  of  many  of  the  companies  in  this 
country  is  that  this  table  gives  results  more  nearly  accurate  than 
any  other  in  use,  and  that  it  is  far  better  adjusted.  Another 
objection  against  it  is,  that  some  of  the  lives  were  assured  in 


OF  LIFE  INSURANCE, 


99 


two  or  more  different  companies,  and  in  the  compilation  of  the 
table  they  would  count  as  so  many  seperate  lives.  Neither  of 
these  objections  appear  to  have  had  much  practical  influence. 
The  fact  still  remains  that  for  many  years  it  was  regarded  as  the 
best  table  of  mortality  in  use,  that  it  has  done  excellent  s<j  vl-e 
during  the  last  thirty  years  and  for  some  time  to  come  will 
probably  be  the  standard  table  in  use  in  the  New  England 
states. 

In  compiling  this  table  some  curious  and  unexpected  results 
were  obtained.  It  was  found  that  the  mortality  from  town  life 
taking  all  ages  together,  was  more  favorable  than  country  life, 
and  that  the  mortality  among  assured  females  was  greater  than 
among  assured  males.  The  first  of  these  results  does  not  appear 
to  have  been  noticed  in  this  country,  and  the  latter  may  be 
attributed  to  defective  medical  examination,  or  that  members  of 
this  class  were  induced  to  insure  because  they  were  conscious 
that  they  were  relatively  short-lived.  The  fact  is  clearly  estab- 
lished by  all  writers  on  vital  statistics  that  the  average  longevity 
of  females  is  fully  equal  to  that  of  males,  and  many  companies 
make  no  distinction  whatever  in  the  risk. 


100 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XXX. 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  AT  THE  END  OF 
VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

//Vrf    i 
year. 
\ 

Stcond 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

6.22 

12.66 

I9-3I 

26.19 

33-30 

40  64 

48.23 

<;6.o7 

21 

6.47 

13-17 

20.09 

27.24 

34-64 

42.27 

50.16 

58-31 

22 

6.74 

I3-71 

20.90 

28-34 

36-03 

,43-97 

52-i7 

60.64 

23 

7-OI 

14.26 

21-75 

29.49 

37-48 

45-74 

54-26 

63.07 

24 

7-3° 

14.84 

22.64 

30.69 

39-0° 

47-59 

56.45 

65.60 

2S 

7.60 

i.v45 

23-56 

3*-94 

40.58 

49-  5  i 

58.73 

68.24 

26 

7.91 

16.09 

24.52 

33-24 

42.24 

5I-52 

61.11 

71.00 

27 

8.24 

16-75 

25-53 

34-6o 

43-96 

53-62 

63-59 

73-89 

28 

8-58 

17-43 

26.  =;S 

36.02 

45-76 

55-Si 

66.20 

76-92 

29 

8-93 

18.16 

27.68 

37-50 

47.64 

58-12 

68.93 

80.09 

30 

9-31 

18.91 

28.83 

39.06 

49-63 

60.54 

71.80 

8345 

31 

97° 

19.70 

30-03 

40.70 

5i-7i 

6308 

74.84 

86.98 

32 

IO.II 

20.54 

3*-3! 

42  43 

53-9' 

65.78 

78.04 

90.72 

33 

10.54 

21.42 

32-65 

44-25 

56  25 

68.63 

81.43 

94.67 

34 

1  1.  CO 

"•35 

34-07 

46.20 

58-71 

7I-65 

85-03 

98.86 

35 

11.48 

23-33 

35-59 

48.25 

61.34 

74-86 

88.84 

103.29 

36 

11.99 

24-39 

37-19 

50-43 

64.11 

78.26 

92.87 

107.92 

37 

12-55 

25-51 

38.90 

52-75 

67.08 

St.  87 

97.09 

112.71 

38 

13.12 

26.69 

40.72 

55-22 

70.20 

85.62 

101.43 

117.61 

39 

13-74 

27.96 

42.65 

57-83 

73-46 

89.48 

105.88 

122.59 

40 

14.41 

29.31 

44.70 

60.55 

76.79 

93-42 

110.36 

127.60 

41 

15.12 

30-73 

46.81 

6^.29 

So.  1  6 

97-35 

114.85 

132.64 

42 

15-85 

32.18 

48.91 

66.04 

83-49 

101.26 

119.32 

137-69 

43 

16.59 

33-59 

51.00 

6873 

66.78 

105.11 

123.80 

142-74 

44 

17-30 

3499 

53-02 

71-38 

90.04 

109.02 

128.28 

147.80 

45 

18.01 

36-36 

55-04 

74-03 

93-34 

112.94 

132.80 

152.91 

46 

18.69 

37-71 

57-05 

76.72 

96.67 

116.90 

I37-3S 

158.08 

47 

iQ-39 

39.10 

59-  i  4 

79-47 

100.09 

120.95 

142.05 

163-37 

48 

2Q.IO 

40-54 

61.28 

82-30 

103-57 

125.09 

146-83 

168.78 

49 

20.86 

42.02 

63-47 

85.19 

107.14 

129.34 

I5I-73 

I74-30 

5° 

21.62 

43  S2 

6v7o 

88.13 

110.79 

I33-67 

156.72 

179-95 

51 

22.39 

4vo6 

67.98 

91.14 

"4-53 

138.09 

161.84 

185.74 

S.2 

23.19 

4663 

70.33 

94.24 

118.34 

142.64 

167.09 

191.66 

53 

24.00 

48.26 

72.74 

97.42 

122.29 

I47-32 

172.47 

i  07.  66 

54 

24.85 

49-94 

75-22 

100.70 

126.35 

152.12 

177-93 

203-75 

55 

25.72 

51-65 

77-78 

104.08 

130-51 

156.98 

183.46 

209.87 

06 

26.61 

53-43 

80.42 

107-55 

1.34-72 

161.90 

189.01 

216.02 

57 

27-56 

55-29 

83-15 

ii  1.07 

138.99 

166.84 

194-59 

222.18 

5S 

28.52 

57-iS 

Ss.88 

II4-59 

142.23 

171.76 

200.  14 

228.28 

59 

29.50 

59-05 

88.60 

118.08 

147.46 

176.66 

205.63 

23^-30 

60 

30-45 

60.90 

91.28 

121.54 

I5I-63 

181.49 

211.02 

240.21 

OF  LIFE  INSURAMV&. 


101 


TABLE  No.  XXX— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  AT  THE  END  OF 
VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thir- 
teenth 
year. 

Four- 
teenth 
year. 

Fifteenth 
year. 

T-wentieth 
year. 

20 

64.17 

72-53 

81.16 

90.07 

99.27 

108.75 

118.56 

172.61 

21     ' 

66.72 

75-41 

84-37 

93.62 

103.17 

113.04 

123.22 

179-43 

22 

69.38 

78.41 

87.72 

97-33 

107.26 

"7-5i 

128.09 

186.57 

23 

72-I5 

8l.« 

91.20 

IO1.2O 

111.52 

122.17 

I33-I9 

194-03 

24 

75-04 

84-78 

94-S5 

105.24 

"5-97 

127.07 

138.52 

20I.8o 

25 

78.06 

88.20 

98.67 

109.47 

120.65 

132.19 

144.12 

209.84 

26 

81.22 

91.76 

IO2.65 

113.92 

125-54 

137-56 

149.99 

218.13 

27 

84.52 

95-50 

106.85 

118-57 

130.69 

143.22 

156.17 

226.62 

28 

87.99 

99-43 

111.25 

123.46 

136.10 

149.16 

162.65 

235.31 

29 

91.64 

103.56 

115.88 

128.62 

141.80 

155-40 

169.41 

244.20 

30 

95-48 

107.91 

120.77 

134.06 

J47-79 

161.93 

176.42 

253.29 

31 

99-53 

112.51 

125.93 

139-79 

154-05 

168.68 

183-65 

262.57 

3^ 

103.82 

"7-37 

131-36 

M5-77 

160.54 

175.66 

191.06 

272.02 

33 

108.36 

122.50 

137-05 

I5I-97 

167.24 

182.80 

198.65 

281.65 

34 

"3-15 

127.86 

142.94 

158-38 

174.10 

190.11 

206.39 

291.42 

35 

118.16 

133-41 

149.02 

164.92 

181.11 

197-57 

214.30 

301.35 

36 

123-35 

i39-'3 

155-22 

171.60 

188.25 

205.13 

222.36 

311.42 

37 

128.69 

M4-97 

161.54 

178-39 

'95-53 

212.92 

230.54 

321.60 

33 

134.10 

150.89 

167.95 

185-31 

202.92 

220.76 

238-83 

33L9I 

39 

139.60 

156.89 

174.47 

192.32 

210.40 

228.71 

247.22 

342-33 

40 

I45-H 

162.97 

181.06 

199.40 

217.96 

236.73 

255.70 

352-84 

4i 

150  73 

169.09. 

187.69 

206.53 

225-57 

244.82 

264.25 

363-37 

42 

156.33 

175-22 

194-35 

213.68 

233-23 

252-95 

272.83 

373-90 

43 

161.94 

181.37 

201.  02 

220  87 

240.92 

261.11 

281.47 

384-39 

44 

167.56 

187.54 

207.73 

228.11 

248.65 

269.36 

290.19 

394-86 

45 

I73-24 

193-79 

214-53 

235-43 

256.50 

277-7° 

299.01 

405-30 

46 

179.12 

200.13 

221.41 

242.86 

264.45 

286.15 

307-S7 

415-71 

47 

184.90 

206.59 

228.45 

250.45 

272.56 

294.71 

316.86 

426.07 

48 

190.90 

213.19 

235-63 

258.18 

280.76 

303.35 

325.89 

436  37 

49 

197.06 

219.95 

242.96 

266.01 

289.07 

312.06 

334-98 

446.62 

50 

203-34 

226.84 

250.38 

273.92 

297.41 

320.81 

344-07 

456.79 

5i 

209.76 

223.82 

257.88 

281.89 

305-81 

329-58 

353-18 

466.88 

52 

216.27 

240.88 

265.44 

289.91 

3H-23 

338.36 

362.24 

476-87 

53 

222.86 

248.00 

273.05 

297-95 

322.65 

347-  19 

37I-25 

486.76 

54 

229.51 

255-18 

280.68 

306.00 

33I-04 

355-7° 

380.21 

496-55 

55 

236.19 

262.35 

288.31 

3I3-99 

339-37 

364.42 

389.11 

506.21 

56 

242.87 

269.52 

295.88 

321-93 

347-63 

372-98 

397-92 

5I5-79 

57 

249-54 

276.63 

303.39 

329.80 

355-84 

38i.47 

406.65 

525-16 

58 

256.  13 

283-65 

3IO.8l 

337-59 

363-94 

389-84 

415.26 

534-43 

59 

262.63 

290.58 

318.14 

345-27 

371-93 

398.09 

423-74 

534-53 

60 

269.02 

297.42 

325-37 

352-84 

379-8o 

406.22 

432.09 

552-49 

102 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXXI. 


NET  VALUE  PER  $1,000  OF  A  TEN-PAYMENT  LIFE  POLICY,  AT  THE  END 
OF  VARIOUS  YEARS.  COMBINED  EXPERIENCE,  4  PER  CENT. 


Agt, 

First 
year. 

Second 
year. 

Third 
year. 

Fotirth 
year. 

Fifth 
year. 

20 

24.94 

50.98 

78.19 

106.61 

136.30 

21 

y" 

25.46 

52.06 

79.84 

108.85 

I39-I7 

22 

26.01 

53-17 

81.54 

111,17 

142,13 

23 

26.57 

54-31 

83.29 

"3-56 

H5  19 

24 

27.14 

55-49 

85.10 

116.03 

148.34 

25 

27.74 

56-7I 

86.97 

118.57 

I5I-59 

26 

2S-35 

57-96 

88.89 

121.19 

154-94 

27 

28.99 

59-26 

90.87 

123.90 

158.40 

28 

29.64 

60.59 

92.91 

12668 

161.95 

29 

30-3I 

61.96 

95.01 

129.54 

165.61 

30 

31.00 

63-37 

97.17 

13249 

169.40 

31 

3I-7I 

64.82 

99.40 

135-53 

17330 

32 

32-44 

66.32 

101.70 

138.68 

I77-32 

33 

33-20 

67.87 

104.08 

141.92 

181.48 

34. 

33-93 

69.46 

106.53 

H5-27 

185.79 

35 

34-7S 

71.11 

109.06 

148.74 

190.23 

36 

35-6i 

72.81 

111.69 

I52-33 

194.84 

37 

36.48 

74-58 

114.41 

156.05 

199.61 

33 

37-37 

76.42 

"7-23 

I59-9I 

204.55 

39 

38-30 

78.32 

120.  l6 

163.90 

209.6! 

40 

39-27 

80.31 

123.20 

167.99 

214-75 

4i 

40.28 

82.36 

126.30 

172.13 

219.96 

42 

4^-32 

84,44 

129-39 

176.27 

225.14 

43 

42.35 

86.48 

132.46  . 

180.36 

230.29 

44 

43-35 

88.49 

135-47 

184.40 

235-4I 

45 

44-34 

9°-45 

138.44 

188.41 

240.52 

46 

45-29 

92-37 

141-37 

192.40 

245.62 

47 

46.25 

94-31 

144.31 

196.41 

250./3 

48 

47-18 

96.22 

147.24 

200.35 

255.80 

49 

48.11 

98.12 

150.15 

204-33 

260.84 

50 

49.06 

1  00.02 

153.03 

208.25 

265.87 

5i 

49-97 

101.88 

155-86 

212  12 

270-83 

52 

50.87 

103  70 

158  67 

215-94 

275-74 

53 

51-75 

105.51 

161.42 

219.70 

280.60 

54 

52-63 

107.28 

164.13 

223.43 

285.37 

55 

53-49 

109.01 

166.81 

227.05 

290.07 

56 

54-?  i 

110.73 

169.40 

230.62 

294.62 

57 
<8 

55-  *6 
55-92 

112.39 
113.98 

171.96 

174-35 

23406 
23730 

299.02 

3°3-i3 

59 

56-71 

"5-51 

176.63 

240.38 

3^7-13 

60 

57-39 

116.88 

178.70 

243-20 

310.78 

OF  LIFE  INSURANCE. 


103 


TABLE  No.  XXXI— (CONTINUED.) 
NET  VALUE   PER   $1.000  OF  A  TEN-PAYMENT    LIFE    POLICY,  AT  Tire 

END    OF    VARIOUS    YEARS.    COMBINED    EXPERIENCE,    4    PER   CENT. 


4** 

Sixth 
year. 

Seventh 

year. 

Eighth 
year. 

Ninth 
year. 

Tfnth 
year. 

20 

167.33 

199-75 

233-65 

269.10 

306.17 

21 

170.85 

203.96 

238.58 

274-77 

312.62 

22* 

174.49 

208.30 

243-66 

280.62 

319.29 

23 

178.24 

212.78 

248.90 

2S6.66 

326.17 

24 

182.12 

217.40 

254-3I 

292.90 

333-27 

25 

1  86.  10 

222.17 

259.88 

299-33 

340.60 

26 

190.21 

227.08 

265.63 

305-97 

348.17 

27 

194-45 

23^15 

27I-57 

312.82 

355-99 

28 

198.82 

237-37 

277.70 

319.90 

364.07 

29 

20333 

242.77 

284.02 

327.20 

372.42 

30 

207.98 

248  33 

290.56 

334-76 

381.04 

31 

212.78 

25408 

297-31 

342-56 

389.96 

32 

217.74 

260.03 

304.28 

350.63 

399.18 

33 

222.87 

266.17 

3"-5° 

358.97 

408.71 

34 

228.16 

272.52 

318.96 

367-59 

41852 

35 

233-64 

279.08 

326.66 

376.45 

4*3-57 

36 

239-32 

285-87 

334-58 

3S5-53 

438.86 

37 

245.  »8 

292.85 

342.68 

394-81 

449-35 

38 

251.21 

299-97 

350-95 

404.25 

460.02 

39 

257-35 

307-23 

359-33 

4I3-83 

470.88 

40 

263.59 

3M-56 

367.82 

423-54 

481.91 

4i 

269.85 

321-94 

376.40 

43338 

493-" 

42 

276.12 

329-37 

385-04 

443-34 

504.46 

43 

282.39 

336.8i 

393-75 

453-38 

5I5-95 

44 

288.65 

344-29 

402.50 

463-51 

527.57 

45 

294.92 

35I-78 

411.29 

473-71 

539-31 

46 

301.18 

354-28 

420.12 

483-98 

551.16 

47 

307-45 

366.78 

428.98 

494-3^ 

563-10 

48 

3t3-7o 

374-29 

437-85 

504.68 

574-  H 

49 

3i993 

381.78 

446.71 

515-09 

587-26 

5° 

326.12 

389-25 

455-62 

525-52 

599-43 

51 

332-26 

396-71 

464-45 

535-95 

611.63 

52 

33«  36 

404  08 

473-26 

546-33 

623-83 

53 

34437 

411.38 

481.97 

556.65 

636.00 

54 

350-32 

418.57 

490.58 

566.88 

648.  1  2 

55 

356-12 

425-62 

499-05 

576.98 

660.17 

56 

36i.77 

432-49 

507-32 

586.92 

672.13 

57 

367.22 

439-  *  4 

515.39 

596.68 

683.96 

53 

372-41 

445-53 

523-18 

606.22 

695.66 

59 

377-35 

451-63 

530-72 

615-50 

707.19 

60 

38196 

457-40 

537-89 

624.51 

718.57 

xo4 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XXXII. 
NET  VALUE  OF  A  TEN- YEAR   ENDOWMENT  POLICY,  AT  THE  END  OF 

VARIOUS  YEARS,   COMBINED  EXPERIENCE,  4  PER  CENT. 


Agt. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

20 

80.51 

164.79 

253.02 

345-41 

442.17 

21 

80.49 

164.74 

252-95 

345-32 

442.07 

22 

.80.46 

164.69 

252.87 

345-23 

441.97 

23 

80.43 

164.63 

252-79 

345^3 

441-85 

24 

80.40 

164.57 

252.71 

345-02 

441-73 

25 

80.37 

164.51 

252.62 

344-91 

441.60 

26 

So-33 

164.44 

252.53 

344-79 

441-47 

27 

80.30 

I64.37 

252.43 

344-66 

44'  32 

28 

80.27 

164.30 

252.31 

344-53 

441.16 

29 

80.22 

164.21 

252.20 

344-3S 

440.99 

30 

80.17 

164.12 

252.06 

344.21 

440.81 

31 

So.  1  2 

164.03 

25I.93 

344.05 

440.63 

32 

80.06 

163.92 

251.78 

343-87 

440-43 

33 

80.OI 

163.82 

251-63 

343-68 

440-22 

34 

79-95 

163.70 

25L47 

343-49 

440.00 

35 

78.89 

163.61 

»5.'-3« 

343.29 

439-79 

36 

79-83 

163.48 

*5MS 

343-" 

439-57 

37 

79.76 

16336 

251.00 

342.92 

439-37 

33 

79.72 

163.27 

2SC.88 

342-77 

439-  -'-1 

39 

79.68 

163.20 

250.78 

342-65 

439-°5 

40 

79-65 

163.16 

250.71 

342-54 

438.87 

4i 

79-65 

I63-I3 

250.64 

342-39 

438-65 

42 

79-65 

163.09 

250.51 

342-17 

438.33 

43 

79.62 

162.98 

250.32 

341-85 

437  -9° 

44 

79-55 

162.82 

250.02 

341-43 

437-38 

45 

79-45 

162.58 

249.63 

340.92 

436.77 

46 

79-30 

162.27 

249  17 

340-33 

436-07 

47 

79.14 

161.94 

248.68 

339.69 

435-32 

48 

78.96 

161.58 

248.14 

338.99 

434-49 

49 

78-77 

161.19 

247-56 

338-23 

433-58 

50 

78.56 

160.80 

246.92 

337-39 

432.60 

5i 

78-33 

160.29 

24(1.21 

336-48 

43I-52 

52 

78.07 

159-77 

245-45 

335-49 

430-3.5 

53 

77-79 

159-22 

244.62 

334-42 

429.  10 

54 

77-51 

158.64 

243-75 

333-29 

427.78 

55 

77.20 

IijS.OO 

242  82 

332-10 

426.36 

56 

76.86 

157-35 

241.86 

330-84 

424.84 

57 

76.55 

156.69 

240.85 

329.48 

423-19 

58 

76.20 

I55.98 

239-74 

327-99 

421-36 

59 

75-84 

I55-I9 

238.50 

326.33 

4I9-35 

60 

75-40 

154.29 

237.12 

324-50 

417.14 

OF  LIFE  INSURANCE. 


I05 


TABLE  No.  XXXII— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TEN- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

Ninth 
year. 

Tenth 
year. 

20 

543-53 

649-72 

761.01 

877-67 

1,000.00 

21 

543-42 

649.62 

760.92 

877.62 

1,000.00 

22 

543-32 

649-5I 

760.84 

877-57 

1,000.00 

23 

543-19 

649.42 

760.77 

877-53 

I,OOO.OO 

24 

543-07 

649.30 

760.67 

877-47 

I,OOO.OO 

25 

542-93 

649.21 

760.55 

877-40 

1,000.00 

26 

54^-79 

649.  1  1 

760.42 

877-31 

1,000.00 

2? 

542-64 

648.87 

760.30 

877.24 

I,OOO.OO 

28 

542-47 

648.71 

760.18 

877.16 

1,000.00 

29 

542-30 

648.55 

760.04 

877.08 

I,OOO.OO 

30 

542.11 

648.38 

759-90 

876.99 

I,OOO.OO 

31 

54I-92 

648.24 

759-80 

876.90 

I,OOO.OO 

32 

54i-7i 

648.00 

759-59 

876.81 

I,OOO.OO 

33 

54I-50 

647.80 

759-43 

876.71 

1,000.00 

34 

541.28 

647-59 

759-25 

876.60 

1,000.00 

35 

541.06 

647.38 

759.09 

876.49 

1,000.00 

36 

540.84 

647.18 

758.91 

876.38 

1,000.00 

37 

540.64 

646.98 

75«-  73 

876.25 

I.OOO.OO 

33 

540-45 

646.77 

758.53 

876.11 

1,000.00 

39 

540.24 

64653 

758-30 

875-95 

1,000.00 

40 

540.00 

646.24 

758.02 

S75-76 

1,000.00 

4» 

539-70 

645.92 

757-71 

875.56 

I.OOO.OO 

42 

539-31 

645  48 

757-32 

8-5-30 

I.OOO.OO 

43 

538.82 

644.98 

756-87 

875  "x 

I.OOO.OO 

44 

538-23 

644.40 

756.37 

874-69 

1,000.00 

4.5 

S37-56 

643-73 

755-79 

874-32 

1,000.00 

46 

536-8i 

642.99 

755-15 

873-92 

1,000.00 

47 

53.S-98 

642.15 

7.)  4-  43 

873-44 

1,000.00 

48 

535  °8 

641  29 

7^-69 

872.99 

I.OOO.OO 

49 

534-10 

6-JO-3I 

752-84 

S72-45 

1,000.00 

50 

533-03 

639-23 

75I-92 

871.86 

I.OOO.OO 

5i 

53«-85 

638.08 

750-94 

871.25 

1,000.00 

52 

530-59 

636.85 

749-87 

870.^6 

1,000.00 

53 

529-24 

635-.SO 

748.70 

869.80 

I.OOO.OO 

54 

527.80 

634.06 

747-44 

868.99 

1,000.00 

55 

526.23 

632.54 

746.11 

868.15 

I.OOO.OO 

56 

524-54 

630.76 

744-53 

867.10 

1,000.00 

57 

522.68 

628.88 

742.88 

866.02 

1,000.00 

53 

520.65 

626.80 

74I-03 

864.81 

1,000.00 

59 

518.41 

624-54 

739-04 

863-51 

1,000.00 

60 

5I5-94 

622.02 

736.80 

862.05 

1,000.00 

io6 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XXXIII. 

NET  VALUE  PER  $1,000  OF  A  FIFTEEN- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

47.42 

97-oi 

148.90 

203.19 

26O.OI 

319.48 

3^-75 

446.95 

21 

47.40 

96.98 

148.85 

203.12 

259.91 

3I9-37 

381.62 

446.80 

22 

47-38 

96.94 

148.79 

203.04 

259.82 

319.26 

381.49 

446.66 

23 

47-36 

96.90 

I4S-73 

202.96 

259-7  l 

319-13 

3Si-34 

446.50 

24 

47-34 

96.86 

148.66 

202.87 

259.61 

319.00 

381.19 

446-33 

25 

47-32 

96.82 

148.60 

202.78 

259.49 

318.85 

381-03 

446.15 

26 

47-30 

96.77 

148.52 

202.68 

259-35 

318.69 

380.84 

4-15-95 

27 

47.27 

96-72 

MS-44 

20.2.56 

259.21 

3I8-52 

380.74 

445-72 

28 

47-25 

96.66 

I4S35 

202.44 

259-05 

318.34 

380.43 

445-50 

29 

47-22 

96-59 

148.25 

202.30 

258.89 

318.14 

380.30 

445-25 

30 

47-18 

96.52 

148.14 

202.16 

258.71 

3I7-94 

379-96 

444-99 

31 

47-15 

96-45 

148.03 

2O2.OI 

258.53 

3I7-72 

379-75 

444-74 

32 

47.11 

96-37 

147.92 

201.87 

258.36 

3J7-52 

379-51 

444-50 

33 

47.07 

96.31 

147.82 

201-73 

258.19 

3i7-3i 

379-30 

444.28 

34 

47-05 

96.25 

147-73 

201.62 

258.05 

3I7-I7 

379-13 

444.10 

35 

47.02 

96.20 

147.66 

201.52 

257-94 

3^7-05 

378.99 

443.96 

36 

47.00 

96.17 

147.61 

201-47 

257.88 

316.99 

378-94 

443.88 

37 

47-00 

96.16 

147.61 

201.46 

257.88 

316.99 

3/891 

443-79 

33 

47.01 

96.18 

147.64 

2OI.52 

257-94 

317.02 

378.88 

443.69 

39 

47.04 

96.24 

H7-73 

201.63 

258.04 

317.06 

378.85 

443-35 

40 

47.08 

96-34 

I47-87 

201.76 

2158.12 

317.06 

3/S.72 

443-31 

4i 

47.16 

96.47 

148.02 

201.87 

258.16 

316.99 

378.54 

443-ot 

42 

47.24 

96-.S9 

148.11 

201.92 

258.09 

316.80 

378-23 

442-58 

45 

47-30 

9665 

148.14 

201.84 

257.90 

3l6-50 

377-So 

442.04 

44 

47-33 

96.66 

148.06 

201.66 

257.61 

316.09 

377-27 

441-39 

45 

47-33 

96.60 

147.91 

201.41 

257-24 

315-59 

376.64 

440.63 

46 

47.28 

96.48 

147.70 

201.09 

256.80 

3i5-oi 

375-92 

439-77 

47 

47-23 

96-35 

147.48 

200.75 

256.32 

3I5-38 

375-13 

438-84 

48 

47.18 

96.22 

147.24 

200.38 

255.80 

313-69 

374-2t 

437-75 

49 

47.12 

96.08 

146.98 

199.98 

255-23 

312.98 

373-36 

436.74 

50 

47.07 

95-93 

146.70 

199-54 

254.64 

312-18 

372-39 

435-62 

5i 

47-oo 

95-76 

146.40 

199.09 

254.00 

3ii-34 

37I-3S 

434-41 

52 

46-93 

95-58 

146.10 

198.62 

253-33 

310.48 

370.32 

433-i6 

53 

46.86 

95-42 

H5-78 

198.13 

252.67 

309.61 

369.24 

431-S3 

54 

46.81 

95-25 

H5-43 

197.66 

252.01 

308.73 

368.08 

430.40 

55 

46.75 

95.08 

M5-I9 

197.21 

25I-35 

307.80 

366.86 

428.87 

56 

46.69 

94.96 

H4-93 

196.78 

250.65 

306.81 

365-54 

427.22 

57 

46.68 

94.87 

144.71 

I96-33 

249.92 

305-74 

364.12 

425.43 

58 

46.67 

94-79 

H4-45 

195.82 

249.10 

304-58 

362.56 

423-47 

59 

46.67 

94-67 

144.14 

195-24 

248.20 

303.28 

360.83 

421.31 

60 

46.63 

94-51 

M3-76 

194.58 

247.18 

301.84 

358.93 

418.93 

OF  LIFE  INSURANCE. 


107 


TABLE  No.  XXXIII— (CONTINUED.) 

NET  VALUE  PER  $1.000  OF  A  FIFTEEN- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Aft. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Tlu'rPnlk 
year. 

Four1  nth 
ytar. 

Fifteenth 
year. 

20 

5I5-24 

•586.80 

661.78 

740-39 

822.8l 

909.28 

1,000.00 

21 

5I5-09 

586.64 

661.62 

740.21 

822.70 

909.20 

1,000.00 

22 

5H-93 

586.48 

661.47 

740.11 

822.59 

909.14 

1,000.00 

23 

5I4-76 

586.30 

661.30 

739-95 

822.47 

909.07 

1,000.00 

24 

514-58 

586.12 

661.12 

739.80 

822.35 

909.00 

I,COO.OO 

25 

514-39 

585-92 

660.93 

739-62 

822.19 

908  90 

I.OOO.OO 

26 

514.18 

5S5-7I 

660.73 

739-44 

822.07 

908.80 

1,000.00 

27 

5I3-94 

585.46 

660.49 

739-23 

821.90 

908-73 

1,000.00 

28 

5I3-70 

585-22 

660.27 

739-03 

821.74 

908.64 

1,000.00 

29 

513-44 

584-97 

660.02 

738-80 

821.59 

908.56 

1,000.00 

30 

5I3-I7 

584.70 

659-77 

738-59 

821.39 

908.43 

1,000.00 

31 

512.91 

584-44 

659-52 

738-37 

821.22 

908.31 

I.OOO.CO 

32 

512.68 

584.21 

659-31 

738.i8 

821.06 

908.23 

1,000.00 

33 

512.45 

583-99 

659.09 

737.96 

820,86 

908.09 

1,000.00 

34 

512.27 

583-79 

658.87 

737-73 

820.66 

907-95 

1,000.00 

35 

512.10 

583-58 

658.63 

737-47 

820.42 

907.79 

1,000.00 

36 

5"-97 

583-4I 

658.40 

737-22 

820.19 

907.65 

1,000.00 

37 

511.81 

583-I6 

658.10 

736-91 

819.90 

907.46 

I.OOO.OO 

33 

511.61 

582.88 

657.76 

736.55 

819.59 

907.25 

1,000.00 

39 

5"-37 

582.56 

657.40 

736-17 

819.26 

907.01 

1,000.00 

40 

5"-03 

582.23 

6156.91 

735-68 

818.82 

906.75 

1,000.00 

4i 

5to.63 

582.66 

656-39 

735-16 

818.37 

906.48 

1,000.00 

42 

510.10 

582.05 

655-73 

734-51 

817.81 

906.12 

1,000.00 

43 

509.46 

580.33 

654.98 

733-79 

817.20 

9°5-74 

1,000.00 

44 

508.70 

579-49 

654.11 

732-96 

816.50 

905-30 

1,000.00 

45 

507.82 

578.54 

653-I4 

732.03 

815.73 

904.81 

1,000.00 

46 

506.86 

577-50 

652.06 

731.02 

814,89 

904.30 

1,000.00 

47 

505.80 

576.35 

650.89 

72991 

8I3-97 

903.72 

1,000.00 

48 

504-56 

575-01 

649.51 

728,58 

812.90 

903.11 

1,000.00 

49 

503-43 

573-So 

648.32 

727-46 

811.88 

902.40 

1,000.00 

50 

502.16 

572.42 

646.86 

727-05 

810.70 

901.66 

1,000.00 

5i 

500.80 

570-91 

645.29 

724-53 

809.41 

900.84 

1,000.00 

52 

499-33 

569-30 

643-59 

722.89 

SoS.oo 

899^5 

1,000.00 

53 

497-78 

567-56 

641.77 

721.11 

806.48 

898.99 

I,COO.OO 

54 

496.  10 

565-68 

639-77 

719-15 

804.80 

897.91 

1,000.00 

55 

494-29 

563-64 

637.61 

7I7-03 

802.97 

896.74 

1,000.00 

56 

492.32 

561.41 

635-24 

714.70 

800.915 

895^5 

1,000.00 

57 

490.19 

559-oo 

632.66 

712.16 

798.76 

894.03 

1,000.00 

58 

487.84 

556.34 

629.82 

709-37 

796-35 

892.48 

1,000.00 

59 

485.26 

553-43 

626.73 

706.33 

793-70 

890.77 

1,000.00 

60 

482.44 

550.26 

626.36 

703.01 

790.82 

888.87 

1,000.00 

io8 


PRINCIPLES  AND    PRACTICE 
TABLE  No.  XXXIV. 


NET  VALUE  PER  $i,coo  OF  A  TWENTY- YEAR  ENDOWMENT  POLICY.  AT 

THE    END  OF  VARIOUS  YEARS,    COMBINED  EXPERIENCE.   4  PER  CENT. 


Age. 

First 
year. 

Second 
year 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

20 

31-39 

64.19 

98.48 

I34-32 

171.80 

210.99 

251.98 

21 

3I-38 

64.18 

98.46 

134.28 

I?i-75 

210.92 

251.89 

22 

3I-38 

64.16 

98.43 

134-25 

171.69 

210.85 

251.80 

23 

31-37 

64.14 

98.40 

134.20 

171.63 

210.76 

251.69 

24 

3I-36 

64.13 

98-37 

134-I5 

171.56 

210.68 

25I-58 

25 

31-35 

64.11 

9S-34 

134.10 

171.49 

210.58 

2.SI-45 

26 

3!-34 

64.09 

98.30 

134.04 

171.40 

210.47 

25I-32 

27 

3i-34 

64.06 

9S-25 

I33-98 

171-32 

210.36 

251.18 

28 

3!-33 

64.04 

98.21 

I33-92 

171.23 

210.25 

25^05 

29 

3I-32 

64.02 

98.17 

133-86 

171-15 

210.15 

250.94 

30 

3i-3i 

64.00 

98.14 

I33-80 

171.09 

210.06 

250.82 

31 

3i-3i 

63-98 

98.12 

I33-78 

171.04 

2IO.OO 

250.7? 

32 

3i-3o 

63-9S 

98.11 

I33-76 

171.03 

209.99 

250.73 

33 

3KV 

64.00 

98.13 

133-79 

171.06 

2IO.O2 

250.78 

34 

31-33 

64.03 

98.18 

133-86 

171.14 

210.13 

250.90 

35 

3I-36 

64.09 

98.27 

133-97 

171.29 

210.31 

251.11 

3f> 

31.40 

64.18 

98.40 

I34-I5 

171.52 

210-59 

251.40 

37 

31-47 

64.30 

9S-59 

I34-4I 

171.84 

210.97 

25I-85. 

38 

3'-54 

64.47 

98.84 

134-75 

172.26 

211.42 

252.24 

39 

3I-65 

64.69 

99.17 

135-lS 

172.74 

211.89 

252.80 

40 

31-79 

64.06 

99-57 

I35.65 

173-23 

212.36 

253.09 

4i 

31.96 

65.28 

99.99 

136.12 

173-73 

212.77 

253-42 

42 

32-14 

65.60 

100.98 

136.54 

174.08 

213.09 

253^5 

43 

32-31 

65.87 

100.71 

136-85 

174-36 

2I3-31 

253-Sl 

44  ' 

32-44 

66.10 

100.96 

137.10 

'74-57 

213-47 

253.87 

45 

32-57 

66.27 

101.16 

I37-29 

174-74 

213-58 

253-9° 

46 

32.61 

66-37 

101-33 

137-47 

174.89 

213.67 

253-90 

47 

32.75 

66.  s  8 

101.53 

I37-67 

175.06 

213-78 

253.90 

48 

32-85 

66.76 

101  76 

I37-90 

175.26 

213.91 

253-95 

49 

32.98 

66.96 

IO2.OI 

138.16 

175-49 

214.08 

254.01 

50 

33-" 

67.19 

IO2.29 

138.45 

175.76 

214.29 

254.13 

5l 

33-25 

67.44 

102-59 

138.77 

17608 

214-55 

254.32 

5-- 

33-44 

67.71 

102-95 

139.18 

176.46 

214.90 

254-59 

53 

33-58 

68.03 

103.36 

J39-64 

176.94 

215.36 

254-96 

54 

33-So 

68.40 

103.84 

140.20 

177-54 

215-92 

255-40 

55 

34-03 

6S.8o 

104.40 

140.86 

178.24 

216.55 

255.90 

56 

34-28 

69.30 

105.07 

141.64 

179.02 

217.26 

256.46 

57 

34.60 

69.87 

105.84 

142.49 

179.87 

218.03 

257.07 

58 

34-95 

70-5I 

106.64 

143-40 

180.76 

218.84 

257-70 

59 

35-33 

7i-i5 

107.47 

144.30 

181.68 

219.67 

258.35 

60 

35-70 

71.80 

108.30 

145.24 

182.62 

220.52 

259.01 

OF  LIFE  INSURANCE. 


109 


TABLE   No.  XXXIV— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TWENTY- YEAR  ENDOWMENT  POLICY,  AT 
THE  END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


4r* 

Eighth 
year. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thirfnth 
year. 

Four1  nth 
year. 

Fift'enth 
year. 

20 

294.86 

339-73 

386.71 

435-87 

487.36 

541.29 

597.82 

657-05 

21 

294-75 

339-6i 

386.55 

435-70 

487.17 

541.09 

597-60 

656.84 

22 

294.6  \ 

339-47 

386.40 

435-52 

486.98 

540.89 

597-39 

656.64 

23 

294-5I 

339-3' 

386.21 

435-32 

486.75 

540.65 

597-15 

656.39 

24 

294.38 

339-i6 

386.03 

435-12 

486.54 

540-45 

596-92 

656.18 

25 

294.21 

33S-97 

385.82 

434-88 

486.28 

540.15 

596.64 

655-90 

26 

294.06 

33^-79 

385.62 

43466 

486.05 

539-93 

596.41 

655.68 

27 

293.80 

338.60 

385.40 

434-42 

485.80 

539-65 

596-I5 

655-43 

28 

293-73 

338.41 

3Sv20 

434-21 

485-57 

539-43 

565-93 

655-2I 

29 

293.61 

338.27 

385.04 

434.04 

485.40 

539-26 

595-76 

655-04 

30 

293-43 

338.13 

384.89 

433-89 

485.24 

539-09 

595-59 

654.86 

31 

29339 

338-04 

3S4-76 

433-8o 

4S5-I5 

538.98 

595-43 

654.64 

32 

293-37 

338.02 

384-79 

433-79 

485.12 

538-90 

595-29 

654.44 

33 

293-43 

338.io 

384-87 

433-84 

485.12 

538.84 

595-15 

654-23 

34 

29^.58 

338-25 

385.0I 

433-93 

485.14 

538.76 

594-98 

653-98 

35 

293.81 

338.47 

385-I7 

434-02 

485.12 

538.64 

594-75 

653.68 

36 

294.21 

338.83 

385.37 

434-14 

485.10 

538-52 

594-56 

653-4I 

37 

294.50 

339-0? 

385.58 

434-20 

485.06 

538.37 

594-28 

6.53-04 

38 

294.86 

339-20 

385.72 

434.22 

484.97 

538.I4 

593-94 

653.60 

39 

295.22 

33968 

385-97 

434-34 

484-85 

537-89 

593-59 

652.14 

40 

295-5I 

339-74 

385-90 

434-H 

484.62 

537-52 

593-07 

65I-54 

4i 

295-75 

339-86 

385-90 

434-oo 

484.34 

537-io 

592-54 

651.90 

42 

295.88 

339-87 

385-77 

433-72 

483.90 

536-53 

59r-83 

650.09 

43 

295-93 

339-8o 

385.56 

433-36 

483.40 

535-S7 

59l-°5 

649.22 

44 

295.89 

339-63 

385-24 

432-89 

482.76 

53507 

590.12 

648.21 

45 

295-79 

339-40 

384-86 

432-34 

482.04 

534-21 

589-13 

647.11 

46 

295.68 

339-»6 

384.47 

43I-7S 

481-32 

533-33 

588.11 

645-97 

47 

295-57 

338-90 

384-03 

431.18 

480.54 

532-38 

586.97 

644.69 

48 

295-49 

338.66 

383-53 

430.60 

479.78 

53I-40 

5S5-79 

643-34 

49 

295.42 

338.45 

383.23 

430.02 

478-95 

530-34 

584-50 

641.86 

50 

295.42 

338.30 

382.92 

429-45 

478.13 

529-24 

583-15 

640.32 

5i 

295-49 

338.21 

382.60 

428.87 

477-2.5 

528.08 

581.71 

638.64 

52 

295.68 

338.14 

382.28 

428.25 

4/6-33 

526.82 

580.15 

636.82 

S3 

295-83 

33S-I2 

38I-97 

427-63 

475-35 

525-48 

578.46 

634  84 

54 

296.09 

338.12 

381.67 

426.98 

474-31 

524-05 

576-65 

632.71 

55 

296.38 

338.14 

381.36 

426.28 

473-20 

522-50 

574.69 

630.42 

56 

296.72 

338.18 

381.04 

425.54 

472.00 

520-85 

572.6o 

627.96 

57 

297.09 

338.23 

380.70 

424.74 

470.72 

519.08 

570.38 

625.33 

58 

297.46 

338.26 

380.30 

423.88 

46936 

517.20 

567-99 

622.51 

59 

297-83 

338-26 

379-8? 

422.98 

467-93 

5^5-22 

565-  <17 

619.42 

60 

298.19 

333.25 

379-44 

422.04 

466.43 

5I3-I3 

562.80 

616.32 

no 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXXV. 


NET  VALUE  PER  $1,000  OF  A  TWENTY-FIVE  YEAR  ENDOWMENT  POLICY, 
AT  THE  END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE.  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

22.19 

45.36 

69.55 

94Sl 

I2I.I8 

148.74 

I77.52 

207.60 

21 

22.20 

45-37 

69-56 

94.81 

I2I.I8 

HS-73 

'77-50 

207.56 

22 

22.21 

45.33 

69-57 

94.82 

121.19 

1^8.72 

177-48 

207-53 

23 

22.21 

45-39 

69.58 

94.84 

1  2  1.  2O 

HS.73 

177-48 

207.51 

24 

22.22 

45-41 

69.61 

94.86 

121.22 

148.74 

177-48 

207.50 

25 

22.23 

45-43 

69-63 

94.88 

121.23 

148.74 

177-47 

207.47 

26 

22.25 

45-46 

69.66 

94.92 

121.27 

148.78 

I77-50 

207.49 

27 

22.27 

45-43 

69.70 

94.96 

121.32 

148.82 

'77-54 

207,52 

28 

22.29 

45-52 

69.74 

95-03 

121.39 

148.90 

177.61 

207.60 

29 

22.32 

45-57 

69.52 

95-10 

121-47 

149.00 

177.72 

207.72 

30 

22-34 

45-63 

69.90 

95-21 

121.  6l 

149-  15 

177.89 

207.92 

3» 

22-39 

45-71 

70.01 

95-36 

121-79 

149.36 

178.14 

2OS.2O 

3-2 

22-43 

45-8o 

70.15 

95-54 

122.  OI 

149.63 

178.46 

208.56 

33 

22.49 

45-93 

70-34 

95-S4 

122-39 

150.08 

178.99 

209.16 

34 

22.58 

46.09 

70.58 

96.12 

122.64 

150.51 

179.49 

209.76 

35 

22.67 

46.27 

70.86 

96.49 

123.21 

151.08 

180.17 

210.52 

36 

22.78 

46.50 

71.20 

96-95 

123-79 

•51-79 

180.99 

211.41 

37 

22.92 

46.78 

7I-63 

97-53 

I24-53 

152.66 

181.95 

2i2.4r 

$ 

23.08 

47.12 

72-I5 

98-23 

125.40 

I53-65 

183.01 

213-49 

39 

23.28 

47-52 

72.76 

99-03 

126.34 

154.69 

184.09 

214-55 

40 

23-52 

48.00 

73-47 

99.92 

127.36 

155-79 

185.20 

215-6=; 

4i 

23-79 

48-53 

74-20 

100.80 

128.34 

156.80 

186.23 

216.66 

42 

24.08 

49.07 

74-94 

101.67 

129.31 

157-74 

187.18 

217.60 

43 

29-39 

49.61 

75-67 

102.54 

130-25 

158.72 

188.30 

218.73 

44 

24-65 

50.10 

76-31 

103.30 

131.10 

'59-75 

189.  -8 

219.72 

45 

24-93 

50-57 

76.96 

104.09 

132.02 

160.76 

190.34 

220.81 

46 

25.16 

51.02 

77.69 

104.93 

132-95 

161.78 

191.42 

221.90 

47 

25-43 

5KS2 

78-30 

105.78 

133-97 

162.91 

192.61 

223.13 

48 

25-7I 

52.06 

79.07 

106.74 

'35-09 

164.14 

'93-93 

224.49 

49 

26.03 

52.66 

79-91 

107.79 

136-31 

165.50 

'95-39 

225.99 

50 

26.36 

53-30 

80.82 

108.92 

I37-64 

166.99 

106.98 

227.68 

5i 

26.73 

54.00 

8  1.  So 

110.17 

139.10 

168.61 

198.76 

229.56 

52 

27.12 

54-74 

82.88 

"2.53 

140.69 

170-43 

200.74 

23  !  -65 

53 

27.54 

55-56 

84.05 

113.00 

142.47 

172.44 

202.93 

233-92 

54 

28.02 

56.46 

85-33 

114.66 

144.44 

174.67 

205.29 

236.38 

55 

2S52 

57-4J 

86-75 

116.46 

146.^8 

177-05 

207.86 

239.01 

56 

29.06 

58-50 

88.30 

118.45 

148.89 

179.60 

210.58 

241.83 

i7 

29.69 

59-71 

90.01 

120.56 

I5L34 

182.31 

213-47 

244.81 

5S 

30.34 

60.96 

9'-77 

122.76 

'53-88 

185-13 

216.49 

247.91 

59 

SI-OS 

62.25 

93.60 

125.03 

156-53 

188.05 

219-59 

251.13    i 

i 

60     31.74 

63-57 

95-46 

127.36 

I59-24 

191.06 

222.80      254.44 

OF  LIFE  INSURANCE. 


Ill 


TABLE  No.  XXXV— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  TWENTY-FIVE  YEAR  ENDOWMENT  POLICY, 
AT  THE  2ND  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Ag<. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thir- 
teenth 
year. 

Four- 
teenth 
year. 

Fifteenth 
year. 

Twentieth 
ytar. 

20 

239.04 

271.90 

306.25 

342.18 

379-76 

419.09 

460.27 

697.64 

21 

238.97 

271.81 

306.14 

342.04 

379.60 

418.91 

460.06 

697-3S 

22 

238.92 

27I-73 

306.04 

34I-91 

379-45 

418.74 

459-87 

697.17 

23 

238.89 

271.68 

305-97 

34I-83 

379-35 

418.63 

459-74 

697.03 

24 

238.86 

271.62 

305.88 

34i-7i 

379-23 

418.48 

459-59 

696.84 

25 

238.81 

271-5? 

3°5-34 

341.66 

379-17 

418.37 

459-  4  * 

696.70 

26 

238.82 

27I-57 

305.80 

341.62 

379-  »o 

418.32 

459-42 

696.54 

27 

238.85 

27I-59 

3o.vS2 

34I-63 

379-10 

418.34 

459-43 

696.39 

28 

23S.93 

271.68 

305-91 

34i-7i 

379-21 

418.46 

459-55 

696.21 

29 

239.06 

271.81 

306.06 

341.89 

379-39 

418.63 

459-7  * 

696.01 

30 

239.27 

272.05 

306.32 

342.18 

379-69 

418.92 

459.94 

655.80 

31 

239-59 

271.41 

306.72 

342.60 

380.10 

419.29 

460.24 

695-59 

32 

240.01 

272.87 

307.22 

343-io 

380.56 

419.68 

460.^2 

695-36 

33 

240.69 

273.62 

307.89 

343-73 

381.15 

420.15 

460.88 

69^.12 

34 

24I-35 

274.30 

308.66 

344-47 

381-78 

420.69 

461.30 

694.84 

35 

242.15 

275.11 

309.42 

345-13 

382.33 

42I.IO 

461.  58 

%4  -51 

36 

243-°7 

276.00  i  310.21 

345-82 

382.90 

421-54 

461.88 

694.05 

37 

244.05 

276.93 

311.07 

346-58 

3S3-54 

422.05 

462.24 

693.63 

33 

245.10 

277.91 

3lI-97 

347-39 

384-23 

422.60 

462.63 

693.24 

39 

246.13 

278.87 

312.82 

348.12 

384-83 

423.04 

462.88 

692.67 

40 

247.17 

279.84 

3I3-75 

348-94 

.3S5-48 

423-54 

463.21 

692.08 

4i 

248.15 

280.76 

314-56 

349.62 

386.03 

423.92 

463.41 

691.31 

42 

249.06 

281.62 

3I5-46 

350.26 

386.63 

424-35 

463-67 

690.63 

43 

250.17 

282.65 

316.26 

35i-oS 

387-21 

424.76 

463.88 

689.77 

44 

251.14 

283.58 

3I7-" 

351-82 

387.81 

425.21 

464.15 

688.89 

45 

252.19 

284.58 

318.01 

352.58 

388.42 

425-64 

464.36 

687-77 

46 

253-29 

285.62 

318.97 

3.S3-46 

389.16 

426.19 

464.68 

686.68 

47 

254-5I 

286.79 

320.09 

354-46 

390.00 

426.81 

465.04 

685.48 

48 

255.86 

288.13 

321-35 

355-6i 

390.96 

427.53 

465.46 

684.17 

49 

257.40 

289.65 

322.80 

356-89 

392.04 

428.34 

465-96 

682.78 

50 

259.12 

?9*-3S 

324-39 

358.32 

393-23 

429-24 

466.51 

681.29 

5» 

261.04 

293.22 

326.14 

359-88 

394-54 

430.24 

467.14 

679.71 

52 

263.14 

295.26 

328.05 

361.60 

395-9S 

431-34 

467-83 

678.05 

53 

265.42 

297.48 

330-13 

363-46 

397-55 

432-54 

468.59 

676.29 

54 

267.89 

299.88 

332.38 

365-47 

399-25 

433-84 

469.44 

674-47 

55 

2"o-54 

302.44 

334-78 

367.62 

401.06 

435-3S 

470.41 

672.56 

56 

273-35 

305-17 

337-34 

369-92 

403.02 

436.82 

471.49 

670.60 

57 

276-33 

308.07 

340.06 

372-37 

405.16 

438.54 

472-72 

668.61 

53 

279-44 

311.09 

342.90 

374-99 

407.44 

440.40 

474.08 

666.  56 

59 

282.66 

314.24 

345-92 

377-77 

409.89 

442.43 

475-61 

664.46 

60 

286.00 

3^7-55 

349-09 

380.71 

412.52 

444.65 

477-30 

1662.31 

112 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXXVI. 


NET  VALUE  PER  $1,000  OF  A  THIRTY- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


A?<. 

First 
year. 

Second 
year. 

Third 
rear. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eiffhth 
year. 

2O 

16.42 

33-54 

51-39 

7O.OO 

89.41 

109.66 

130.78 

152.81 

21 

16.45 

33-6o 

51.48 

7O.II 

89-55 

109.87 

130.90 

J52-95 

22 

16.47 

33-64 

51-53 

70.l8 

89.62 

109.88 

I3I-03 

153.08 

23 

16.50 

33-69 

51.61 

70.28 

89-75 

1  10.03 

131.19 

r53--4 

24 

16.54 

33-77 

5I-7I 

70.41 

89.90 

110.21 

I3I-37 

153-44 

25 

16.58 

33-35 

5I-S3 

70.56 

90.08 

110.41 

131.60 

153-68 

26 

16.63 

33-94 

51-97 

70.74 

90.29 

110.65 

131.87 

I53-98 

2l 

16.68 

34-04 

52.12 

70.93 

90.52 

110.92 

132.19 

J  54-33 

28 

16.74 

34-15 

52.28 

71.14 

90.77 

III.  21 

I32-5I 

J54-70 

29 

16.82 

34-31 

52-5I 

71-45 

91.16 

1  1  1.  66 

I33-03 

I55-27 

30 

16.89 

34-46 

52.73 

71-73 

9L5I 

112.  IO 

*33-54 

155-87 

31 

16.99 

34-65 

53-oi 

72.11 

91.98 

112.67 

I33-2I 

156.64 

32 

17.09 

34.86 

53-33 

72-54 

92.52 

"3-32 

134-97 

*57-52 

33 

17.22 

35-" 

53-7i 

73-05 

93-17 

114.10 

!35-S9 

158.59 

34 

17-37 

35-4i 

54.16 

73-66 

93-93 

"5.03 

136.99 

159.86 

35 

1753 

35-74 

54-67 

73-34 

94.80 

116.09 

138-24 

161.29 

36 

J7-73 

36-15 

55-28 

75-17 

95-85 

ii7-39 

J39-83 

162.95 

37 

17.96 

36-61 

55-98 

76.11 

97-05 

118.80 

141.36 

164.72 

3$ 

lS.22 

37-13 

56.78 

77.20 

98.41 

120.37 

143.11 

166.61 

39 

18.52 

37-75 

57-73 

78.46 

99-93 

122.06 

144.96 

168.54 

40 

18.87 

38.45 

58-77 

7980 

101.52 

123.91 

146.95 

17065 

4i 

19.26 

39-23 

59-89 

81.20 

103.16 

125-73 

148.92 

J72-75 

42 

19.68 

40.03 

61.02 

82.61 

104.79 

I27-55 

150.91 

174.84 

43 

2O.  II 

40.82 

62.14 

83-99 

106.41 

129.38 

152-93 

177.07 

44 

20.52 

41.61 

63.22 

85-37 

108.04 

131-25 

i55-oi 

I79-3I 

45 

20.94 

42.38 

64-33 

86.77 

109-73 

133-21 

I57-I9 

181.69 

46 

21-34 

43-i6 

65-45 

88.24 

111.51 

135-26 

!59-4S 

184.19 

47 

21.76 

43-99 

66.68 

89.83 

"3-43 

137-47 

162.01 

186.90 

48 

22.22 

44.88 

67.99 

91.52 

115.48 

I39-84 

164.62 

189.82 

49 

22.72 

45-85 

69.40 

93-36 

117.67 

H2-39 

167.49 

192.96 

50 

23-25 

46.88 

70.90 

95.28 

1  20.02 

145.12 

170.^6 

196.36 

5i 

23.81 

47-97 

73-49 

97-35 

122.54 

148.04 

173-87 

200.02 

5-' 

24.40 

49-13 

74.19 

99-56 

12^.22 

151.19 

J77.45 

203-95 

53 

25-03 

50.37 

76.01 

101.91 

128.11 

J54-57 

181.26 

208.13 

54 

25-7I 

5I-70 

77-94 

104.46 

131.21 

158.18 

185.30 

2  '  -'.53 

55 

26.42 

53-o8 

So.oi 

107.16 

I34-51 

161.97 

189.53 

217.12 

•a 

1 

1 

OF  LIFE   INSURANCE. 


TABLE  No.  XXXVI.— (CONTINUED.) 

NET  VALUE  PER  $1,000  OF  A  THIRTY- YEAR  ENDOWMENT  POLICY,  AT  THE 
END  OF  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CEXT. 


4e*. 

Ninth 
year. 

Tenth 
year. 

Eleventh 
year. 

Twelfth 
year. 

Thir- 
teenth 
year. 

Four- 
teenth 
year. 

Fifteenth 
year. 

Twentieth 
year. 

20 

175.81 

199.81 

224.87 

25I-03 

278.34 

306.89 

336.72 

507.81 

21 

175-93 

199.92 

224.97 

251.11 

278.42 

306.95 

336.77 

507.80 

22 

176.08 

2OO.O7 

225.12 

251.26 

278-56 

307.08 

336.89 

507.90 

23 

176.24 

200.24 

225.28 

251.42 

278.72 

307-23 

337-04 

508.03 

24 

I76-45 

200.45 

225.50 

251.64 

278.94 

307.46 

337-27 

508.26 

25 

176.71 

200.73 

225.79 

251.94 

279.26 

307-79 

337-61 

508.57 

26 

177.04 

2OI.O8 

226.18 

252.36 

279-72 

308.29 

338.15 

509.08 

27 

177.42 

201.49 

226.51 

252.82 

280.20 

308.80 

339-02 

509.35 

28 

177.89 

202.03 

227.14 

253-47 

280.90 

309-55 

339-49 

509.84 

29 

178.47 

202.66 

227.89 

254.22 

281.72 

310.43 

340-35 

510.31 

30 

IK-IZ 

203.42 

228.64 

255-I6 

282.72 

311.46 

341-39 

510.86 

31 

l8o.O2 

204.40 

229.82 

256.34 

283.95 

312.70 

342.60 

511.42 

32 

181.03 

205.52 

231.06 

257-63 

285.27 

3I3-99 

343-8i 

5"-99 

33 

182.24 

206.87 

232.49 

259.  1  1 

286.74 

3*5-40 

345-15 

512.65 

34 

183-67 

208.42 

234.10 

260.75 

288.34 

316.95 

346-61 

5I3-40 

35 

185.24 

210.06 

235-79 

262.41 

289.97 

318.50 

348.08 

514.11 

36 

iSy.OI 

211.91 

237-65 

264.26 

291.78 

320.26 

349-75 

5i4-9i 

37 

188.88 

213.81 

239-56 

266.15 

293-63 

322.04 

35^-43 

5I5-70 

•33 

190.86 

215.84 

241.60 

268.19 

295-63 

323-98 

353-27 

516.68 

39 

192.91 

217.94 

243-73 

270.31 

297.72 

326.00 

355-i8 

5I7-68 

40 

I95-03 

220.12 

245.94 

272.152 

299.89 

328.04 

357-19 

518.75 

4i 

I97-23 

222-39. 

248.25 

274.83 

302.17 

333-32 

359-32 

519.90 

42 

199.48 

224.72 

250-63 

277.22 

304-54 

332-63 

361.27 

521.10 

43 

201.79 

227.12 

253.08 

279.70 

307.01 

335-04 

393-44 

522.34 

44 

204  18 

229.62 

255.66 

282.31 

309.62 

337-67 

366.39 

523-65 

45 

206.70 

232.27 

258.40 

28^.10 

312.42 

340.42 

369.20 

525-05 

46 

209.40 

235-10 

261.32 

288.11 

3I5-47 

343-44 

372.03 

526.56 

47 

212.30 

238.16 

264.51 

291.40 

318.80 

346.72 

375-20 

528.19 

48 

215-43 

241.50 

268.01 

294.97 

322.38 

350.25 

378.60 

529.96 

49 

218.84 

245.11 

271.78 

298.82 

326.24 

354-04 

382.26 

53I-87 

50 

222.51 

249.02 

275.81 

302.94 

330-35 

358-09 

386.17 

533-97 

5i 

226.47 

253-I8 

280.13 

307-3I 

334-73 

362.39 

370-31 

536-25 

52 

230.68 

257.61 

284.70 

311.96 

339-37 

366.95 

394-71 

538.74 

53 

235-H 

262.28 

289.45 

316.85 

344.26 

371-75 

399-34 

541.46 

54 

239.84 

267.20 

294.59 

321.99 

349-39 

376.78 

404.22 

544-41 

55 

244-74 

272.32 

299.86 

327-34 

354-72 

382.04 

409-34 

S47-6i 

PRINCIPLES  AND  PRACTICE 


TABLE  No.  XXXVII. 

NET  ANNUAL  PREMIUMS  PER  $1,000  FOR  JOINT  LIFE  POLICIES,  COM- 
BINED EXPERIENCE,  4  PER  CENT. 


Younger 
Age. 

Equal 
ages. 

Difference 
in  ages. 
$  years. 

Difference 
in  ages. 
10  years. 

Difference 
in  ages. 
15  years. 

Difference 
in  ages. 
20  years. 

Difference 
in  ages. 
25  years. 

Difference 
in  ages. 
30  years. 

!i 

17 
18 

19 
2O 
21 

22 
23 
24 

a 

27 
28 
29 
30 

31 
32 
33 
34 

3I 
36 

37 
38 
39 
40 

4i 
42 

43 
44 

% 

I9.I7 
19.52 
19.90 
20.30 
20.71 
21.14 
21.  60 
22.O7 
22-57 

23.10 
23-65 
24-23 
24.84 
25.48 
26.16 
26.87 

27-63 
28.42 
29.25 

30.14 
31.08 
32.07 

33-'3 
34-25 
35-45 
36.73 
38.11 
39-58 
41.17 
42.87 
44.69 
46  62 

20.20 

20.61 

21.04 
21.48 
21.96 
22-45 
22-97 
23-52 
24.10 
24.70 

25-34 
26.01 
26.71 
27.46 
28.24 
29.07 

29-95 
30.88 
31.86 
32.91 

34-03 
35-22 

36.49 

37.85 
39-31 
40.86 
42.52 
44.29 
46.18 
48.20 

50.35 

C.2  67. 

21.  6l 
22.09 

22.59 
23.12 
23.68 
24.26 
24.88 

25-53 
26.21 
26.93 
27.69 
28.50 

29-35 
30.25 
31.21 
32-23 
33-32 

34-47 
35-70 
37.02 
38-42 

39-9° 
41.48 
43.16 

44-94 
46.84 
48.87 
5I-03 

53-34 
55-So 
58.43 

6l   27 

23-5I 
24.09 
24.71 

25-35 
26.03 

26.75 
27-5I 
28.31 
29.16 
30.06 
31.02 
32.04 
33-13 
34-29 
35-52 
36.83 
38.23 
39-70 
41.26 
42.91 
44.67 

46.53 
48.50 
50.62 
52.86 

55-25 
57-80 

60.53 
63-45 
66.57 
69.92 

77  48 

26.09 
26.82 

27-59 
28.41 

29-27 
30.20 

3I-I7 
32.22 

33-33 
34-52 
35-78 
37-" 
38.53 
40.02 
41.61 

43-29 
45.06 

46.95 
48.95 
51.08 

53-33 
5.5-74 
58-30 
61.02 

63-94 
67.06 

70-39 
73-95 
77-75 
81.83 
86.17 

29-62 
30.58 

31-59 
32.68 

33-83 
35-06 
36.36 

37-73 
39-^9 
40-73 
42.36 
44.10 

45-93 
47-88 
49.94 
52-13 
54-46 
56-94 
59-58 
62.39 

65-38 
68.58 
71.98 
75-6i 
79.48 
83-61 

34-55 
35-82 
37-i8 
38.61 
40.13 
41-73 
43-43 
45-24 
47-15 
49.18 

5i-33 
53-62 
56-05 
58.64 
61.40 
64-34 
67-47 
70.78 

74-35 
78-13 
82.15 

4.7 

48.68 

cc  06 

64.21 

77.  2O 

is 

TO.  86 

JJ 
C.7  6C 

67.7Q 

8l    14 

4.0 

c,7.i8 

60  40 

7O.78 

8s.  67 

CQ 

cc.64 

67  7.2 

74  41 

90.28 

CT 

c.8  26 

78  27 

C2 

61  o? 

60  76 

82  40 

C3 

64  02 

T7   7O 

86  79 

C.4. 

6?.i7 

77  08 

01.48 

ce 

•7O   C4 

8l    17 

06  48 

c6 

•7  A  17 

C7 

•77  06 

82  oc 

CQ 

86  44 

y^-y/ 

ino  27 

6? 

OI    17 

Tor  Rc 

61 

62 

TOI    CO 

67. 

IO7  22 

64 

117   77 

6c 

OF  LIFE  INSURANCE.  115 

TABLE   No.    XXXVIII. 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  JOINT-LIFE  POLICY,  (  EOJJAL 
AGES,)  COMBINED  EXPERIENCE,  4  PER  CENT. 


Aft. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7-57 

15-39 

23-47 

31.80 

40.40 

49.29 

58.46 

67.92 

21 

7.88 

1  6.  02 

24.42 

33-09 

42.04 

51.28 

60.8  1 

70.64 

22 

8.21 

16.67 

25.41 

34-44 

43-74 

53-35 

63.26 

73-48 

23 

8-53 

17-34 

26.45 

35-83 

45-*2 

55-51 

65.81 

76.44 

24 

8.87 

18.07 

27-53 

37-31 

47.3S 

57-77 

68.47 

79-51 

2.5 

9.26 

18.81 

28.67 

38.84 

49-32 

60.12 

71.26 

82-73 

26 

9.64 

19-59 

29-85 

40-43 

51-34 

62.58 

74-15 

86.09 

26 

10.05 

20.41 

31.09 

42.10 

54-45 

65.14 

77.20 

89-63 

2S 

10.46 

21-25 

32-37 

43-84 

55-r'5 

67-83 

80.39 

93-35 

29 

10.90 

22.14 

33-73 

45-67 

57-97 

70-67 

83.76 

97.28 

30 

11.36 

23-08 

35-H 

47.58 

60.42 

73-66 

87.33 

101.44 

31 

11.85 

24.05 

36.64 

49-63 

63.02 

76.84 

91.12 

105.86 

32 

12.35 

25.09 

38-23 

5I-78 

65-77 

80.22 

95-  14 

110.57 

33 

12.89 

26.20 

39-92 

54-°9 

68.72 

83-83 

99-45 

115.62 

34 

13.48 

27.38 

41-73 

56-55 

71.86 

87.68 

104.07 

1  2  I.  O2 

35 

14.09 

28.63 

43-66 

59.18 

75-22 

91.82 

109.01 

126.76 

36 

14-75 

29.99 

45-73 

62.00 

78.84 

96.27 

114.28 

132.80 

3S 

15-47 

3i-44 

47-96 

65-05 

82.74 

101.02 

119.82 

I39-°4 

3§ 

16.23 

33-oo 

50-36 

68-33 

86.90 

105.99 

I25-51 

145.40 

39 

!7-o5 

34-70 

52-96 

71.84 

91.24 

111.09 

'3I-31 

I5I-79 

•4° 

17-95 

36-53 

55-73 

75.48 

9S-67 

II6.24 

137.08 

158.16 

4i 

18.92 

38-47 

58.57 

79-  *3 

100.08 

121.30 

142.77 

164.45 

42 

'9-93 

40.42 

61.37 

82.73 

104-35 

126.23 

148.34 

170.64 

43 

20.91 

42-29 

64.08 

86.14 

io8.<ji 

131.02 

153-78 

176.71 

44 

21.83 

44.09 

66.62 

89-43 

112.46 

I35-7I 

I59.I3 

182.69 

45 

22.75 

45-79 

69.10 

92.65 

116.41 

140.36 

164.44 

188.63 

46 

23-58 

47-43 

71-52 

95-S4 

120.33 

144.99 

169.74 

I94-56 

47 

24-43 

49.11 

74.01 

99.10 

124-35 

149.70 

I75-" 

200.59 

48 

25-29 

50.82 

76-54 

102.42 

128.41 

154.46 

180.57 

206.69 

49 

26.19 

52-58 

79-13 

105-79 

132-51 

I59-3I 

186.10 

212.86 

50 

27.10 

54-36 

81.74 

109.18 

I3'1"?! 

164.21 

191.69 

219.16 

5* 

28.02 

56-16 

84-37 

112  65 

140.93 

169.18 

197.41 

225-57 

52 

28.95 

57-97 

8707 

Il6.l7 

145-23 

174.28 

203.25 

232.10 

53 

29.89 

59-86 

89.82 

119.74 

149  66 

I79.49 

209.21 

238.66 

54 

30.89 

61.77 

92.62 

123.46 

154.22 

184.84 

215.21 

245.25 

55 

31-87 

63.70 

95-52 

127.26 

158.86 

190.27 

221.20 

251.77 

56 

32.88 

65-75 

98-53 

131.18 

163.53 

195.56 

227.14 

258.25 

57 

33-98 

67.88 

101.63 

135-  I  3 

168.21 

200.87 

233-03 

264.61 

58 

35-09 

70.02 

104.67 

I38-95 

172.76 

206.05 

238-74 

270.75 

59 

36.22 

72.11 

107.64 

142.67 

177.16 

211.06 

244-23 

276.65 

60 

37-25 

74.11 

110.46 

146.26 

181.41 

215.69 

249-47 

282.23 

n6 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XXXIX. 


NET  VALUE  PER  $1,000  OF  AN  ORDINARY  JOINT-LIFE  POLICY  (DIFFER- 
ENCE IN  AGES,  FIVE  YEARS),  COMBINED   EXPERIENCE,  4  PER  CENT. 


Is 
§"<5 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eiffhth 
year. 

20 

6.92 

14.08 

21.48 

29.13 

37-03 

45-19 

53-62 

62.32 

21 

7.21 

14.66 

22.37 

30.32 

38-54 

47-02 

55-78 

64.82 

22 

7-51 

I5-27 

23.28 

3I-56 

40.11 

48-93 

58.03 

67.42 

23 

7-82 

15.89 

24.23 

32.86 

41-73 

50.90 

60.36 

70.13 

24 

8.14 

16.55 

25.22 

34.18 

43-43 

52.96 

62.80 

72-95 

25 

8.48 

17.22 

26.26 

35-58 

45-19 

55-" 

65-34 

75-89 

26 

8.82 

17-93 

27-33 

37-03 

47.04 

57-35 

67.99 

78.96 

27 

9.19 

18.67 

28.46 

38-55 

48.96 

59-  '9 

70.76 

82.18 

28 

9-57 

19.44 

29.63 

40.14 

50-97 

62.14 

73-66 

85-54 

29 

9-97 

20.26 

30.86 

41.80 

53-o8 

64.71 

76.71 

89.09 

30 

10.39 

21.  IO 

32.15 

43-54 

55-30 

67.41 

79.91 

92.81 

31 

10.83 

21.98 

33-50 

45-38 

57.62 

70.25 

83.29 

96-75 

32 

11.29 

22.92 

34-93 

47-3  ! 

60.08 

73.26 

86.86 

100.91 

33 

11.77 

23.91 

-  36.43 

49-35 

62.68 

76.44 

90.65 

105-33 

34 

12.29 

24.96 

3803 

5i-52 

65-44 

79-82 

94.68 

1  10.04 

35 

12.83 

26.06 

39-72 

53-8i 

68.37 

83.42 

98.97 

115.04 

36 

i3-4i 

27.24 

41.52 

56-27 

7I-5I 

87.26 

103-54 

120.32 

37 

14.02 

28.49 

43-44 

58.89 

74-86 

91.36 

108.34 

125-83 

38 

14.68 

29.84 

45-51 

61.70 

78.40 

95-69 

114.40 

I3I-58 

39 

15-39 

31.29 

47-73 

64.71 

82.22 

IOO.2O 

118.65 

I37.5I 

40 

16.15 

32.85 

50.10 

67.87 

86.14 

104.88 

124.03 

143.61 

4i 

16.97 

34-50 

52-57 

7i-i3 

90.18 

109.66 

129-55 

149.80 

42 

17.84 

36.22 

55-io 

74.48 

94-29 

114.52 

i35-*3 

156.05 

43 

18.71 

37-94 

57-67 

77-84 

98.44 

119.42 

140.72 

162.29 

44 

19-59 

39-70 

60.25 

81.25 

102.63 

124-33 

146.32 

168.50 

45 

20.51 

4i-47 

62.89 

84.69 

106.83 

129.26 

151.89 

174.69 

46 

21.40 

43-27 

65-53 

88.13 

111.03 

I34-I3 

I57-4I 

180.83 

47 

22.34 

45-09 

68.19 

91.58 

115.19 

138.98 

162.91 

186.98 

48 

23.27 

46.89 

70.82 

94-97 

119.30 

I43-78 

168.40 

193.10 

49 

24.19 

48.69 

73-41 

98.32 

123-38 

148.59 

173-88 

199.22 

50 

25.11 

50.44 

75-97 

101.65 

127.48 

I53-40 

179-37 

205.39 

5i 

25-99 

52-17 

78.52 

105.01 

131.60 

158.24 

184.92 

211.  60 

52 

26.89 

53-93 

81.13 

108.43 

I35-78 

163.18 

I90-57 

217.94 

53 

27-79 

55-75 

83.80 

111.90 

140.06 

168.20 

196.32 

224.30 

54 

28.75 

57.60 

86.51 

"5-47 

144.42 

173-35 

202.13 

230.73 

55 

29.71 

59-47 

89.29 

119.10 

148.87 

178.51 

207-95 

237.64 

56 

30.68 

61.41 

92.13 

122.82 

I53-36 

183.71 

213.82 

243.64 

57 

3i-7o 

63.40 

95.06 

126.56 

157-87 

188.94 

219.71 

250.11 

58 

32-73 

65-43 

97-97 

130.30 

162.38 

194.16 

225.56 

2:56.48 

59 

33-So 

67.44 

100.87 

134.04 

166.89 

199-35 

231.32 

262.74 

60 

34-82 

69.41 

103-74 

137-74 

I7I-34 

204.43 

236.94 

268.79 

OF  LIFE  INSURANCE. 


117 


TABLE  No.  XL. 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  JOINT-LIFE  POLICY,  (  DIFFER- 
ENCE IN   AGES,   TEN   YEARS,)  COMBINED  EXPERIENCE,  4  PER  CENT. 


Older 
Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

25 

7-93 

16.14 

24-59 

33-34 

42-35 

51.69 

61.31 

71.24 

26 

8.26 

16.80 

25.61 

34-70 

44.11 

53-81 

63.82 

74.14 

27 

8.61 

I7-50 

26.66 

36-16 

45-93 

56.02 

66.43 

77-18 

28 

8.97 

18.21 

27.78 

37.65 

47.82 

58.32 

69.16 

So-35 

29 

9-32 

18.99 

28.94 

39.21 

49.80 

60.72 

72.03 

83-69 

30 

9.76 

19.80 

30.17 

40.86 

51.90 

63-30 

75-07 

87.22 

31 

10.14 

20.61 

3I-4I 

42.56 

54-07 

65-95 

78.23 

90.90 

32 

10.58 

21.49 

32-75 

44-3S 

56-38 

68.78 

81.58 

94.82 

33 

11.03 

22.41 

34.16 

46.30 

58.81 

71.77 

85.14 

98.96 

34 

11.51 

23.40 

35-66 

48-34 

61.42 

74-94 

88.91 

103-35 

35 

12.  02 

24-43 

37-25 

50-49 

64.17 

78.30 

92.9I 

108.00 

36 

12.56 

25-54 

38.94 

52.78 

67.07 

81.87 

97.14 

112.88 

37 

I3-H 

26.71 

40-73 

55-22 

70.19 

85.68 

101.58 

117.92 

38 

13-75 

27-95 

42.64 

57-81 

73-50 

89.61 

106.18 

123.14 

39 

14.40 

29.29 

44.68 

60.59 

76.92 

93-72 

110.91 

128.46 

40 

15.10 

30.72 

46.84 

63-43 

80.47 

97.92 

115.72 

133-89 

41 

I5-S5 

32.22 

49.07 

66.37 

84.08 

102.16 

120.61 

I39-4I 

42 

16.63 

33-75 

51-33 

69-33 

87.70 

106.44 

125-54 

145.01 

43 

17.41 

35-29 

53-59 

72.27 

9'-33 

110.75 

130.55 

150.71 

44 

18.19 

36.82 

55-83 

75-23 

95-oo 

115.14 

135-66 

156.53 

45 

18.98 

38-34 

58.10 

78.22 

98.75 

119.64 

140.90 

162.  ijo 

46 

19.74 

39-88 

60.40 

81.32 

102.61 

124.29 

146.31 

168.61 

47 

20-55 

41.48 

62.82 

84-55 

106.65 

129.12 

151.87 

174.87 

48 

21-37 

43.16 

65-34 

87.92 

110.85 

134.08 

I57-56 

181.23 

49 

22.26 

44-98 

67.99 

9*-43 

"5-i7 

139.16- 

i63-35 

18765 

50 

23.19 

46.78 

70.74 

95.02 

"9-57 

144.30 

169.15 

194-13 

51 

24-15 

48.69 

73-54 

98.67 

123-99 

H9-43 

175.00 

200.63 

52 

25.14 

50.61 

76.36 

102.31 

128.38 

I54-58 

180.84 

207.15 

53 

26.13 

52-54 

79.16 

105.90 

'32-77 

I59-72 

186.70 

213-63 

54 

27.12 

54-45 

81.92 

109.51 

I37-I7 

164.88 

192.53 

220.08 

55 

28.10 

56-32 

84.46 

113.12 

141.60 

170.02 

198.34 

226.47 

56 

29.04 

58.22 

87.48 

116.78 

146.03 

175.16 

204.  1  1 

232.83 

57 

30-05 

60.19 

9°-37 

120.48 

150.49 

180.30 

209.88 

239-17 

58 

31-07 

62.18 

93-23 

124.17 

154-yi 

185.40 

215-59 

245-41 

59 

32.11 

64.16 

96.08 

127.81 

159-28 

190.46 

221.22 

251-56 

60 

33-" 

66.10 

98.87 

I3I-39 

163-59 

I95-38 

226.73 

257-59 

Il8  PRINCIPLES  AND  PRACTICE 

TABLE  No.  XLI. 

NET  VALUE  PER  $1,000  OF  AN  ORDINARY  JOINT-LIFE  POLICY,  (.DIFFER- 
ENCE IN    AGES,  FIFTEEN    YEARS,)  COMBINED  EXPERIENCE,  4  PER  CENT. 


Old- 
tr 
age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eiffhth 
year. 

30 

9.28 

18.88 

28.80 

39-04 

49.62 

6o-55 

7I-85 

83-52 

31 

9.69 

19.70 

30.03 

40.72 

51-75 

63-I5 

74-93 

87.10 

32 

IO.  II 

20.54 

3J-33 

42.47 

53-9S 

6c.88 

79.17 

90.88 

33 

10.54 

21.44 

32.70 

44-32 

56.34 

68.76 

Si.  60 

94.89 

34 

11.02 

22.39 

34-  14 

47.29 

59-84 

71.82 

85-25 

99.14 

35 

II.50' 

23-38 

35-66 

48.35 

61.48 

75.06 

89.11 

103.63 

36 

I2.O2 

24-45 

37-29 

50.56 

64.30 

78-51 

93.20 

108-33 

37 

12.58 

25-54 

39.01 

52.92 

67.30 

82.17 

97  48 

113.20 

38 

13.16 

26.77 

40.85 

55-42 

70.48 

85-99 

101.90 

118.20 

39 

13-79 

28.06 

42.82 

58.08 

73.80 

89.92 

106.44 

123.28 

40 

14.47 

29.44 

44.91 

60.85 

77-20 

93-94 

111.02 

128.43 

41 

I5-I9 

30.89 

47-05 

63-65 

80.64 

97-97 

115.72 

133-60 

42 

15-94 

32-36 

49.21 

66.46 

84.06 

101.99 

120.24 

138.82 

43 

16.68 

33-Si 

5i-34 

69.22 

87.44 

105.99 

124.87 

144.06 

44 

17.41 

35-24 

53-43 

71.96 

90.82 

1  10.03 

129.54 

H9-35 

45 

18.15 

36-65 

55-51 

74.71 

94-25 

114.11 

134.28 

154-75 

46 

18.85 

38.06 

57-6i 

77-51 

97-74 

118.28 

139.12 

160.25 

47 

19.58 

39-5° 

59-79 

80.40 

101.34 

122.59 

144.12 

165-95 

48 

20.33 

41.01 

62.04 

83.40 

105.07 

127.03 

149.30 

171.84 

49 

21.12 

42.58 

64-38 

86.50 

108.92 

131-65 

154.66 

177-94 

50 

21-93 

44.20 

66.80 

89.69 

112.91 

136.42 

160.21 

184.27 

5i 

22.77 

45-87 

69.29 

93-03 

117.06 

141.38 

165.98 

190.80 

S2 

23.64 

47.60 

71.89 

96.49 

121.38 

146-55 

171-95 

197.49 

53 

24-54 

49.42 

74.61 

100.10 

125.89     151.90 

178.09 

204.26 

54 

25-5I 

51-33 

77-46 

103.90 

130-56 

I57-38 

184.24 

211.06 

55 

26.50 

53-31 

80.44 

107.80 

135-32 

162.89 

190.41 

217.81 

56 

27-54 

55-41 

83-52 

in-79 

140.  10 

168.37 

196.52 

224.51 

57 

28.66 

57-56 

86.63 

"5-75 

144.81 

I73-76 

202.54 

232.10 

58 

29.76 

59.68 

89.66 

"9-59 

149-39 

179.02 

208.41 

237-5I 

59 

30.84 

61.74 

92-59 

123.30 

I53-84 

184.14 

214.12 

243-74 

60 

31.88 

63.70 

95-40 

126.91 

158.17 

189.11 

219.67 

249.78 

61 

32.87 

65.61 

98.16 

130-45 

162.41 

193.98 

225.08 

255.68 

62 

33-85 

67-5I 

100.89 

!33-94 

166.58 

198.74 

230.38 

261.50 

63 

34-84 

69-39 

103-59 

I37-30 

170.67 

203.42 

235.63 

267.23 

64 

35-80 

71.24 

106.25 

Ho.73 

174.67 

208.04 

240.78 

272.86 

65 

36.75 

73.06 

108.83 

144.02 

178.63 

212.59 

245.68 

278.42 

COST   OF   INSURANCE. 


COST  OF  INSURANCE. 

These  tables  for  the  cost  of  insurance,  give  the  tabular  value 
of  carrying  the  risk  of  a  policy  of  $1.000  for  various  ages  and 
conditions,  and  during  the  first  eight  years  it  is  in  force,  and 
they  are  computed  on  the  American  Experience  Table  of  Mor- 
tality, 4£  per  cent  interest,  and  on  the  Combined  Experience 
4  per  cent. 

Since  the  Contribution  Plan  for  dividing  the  surplus  has  been 
generally  adopted,  the  cost  of  insurance  has  become  one  of  the 
most  important  subjects  of  computation.  It  shows  the  tabular 
expense  a  company  incurs  in  carrying  a  policy  a  year,  and  is  an 
important  aid  in  finding  what  should  be  the  surrender  charge. 
By  comparing  the  cost  of  insurance  for  a  given  age  in  different 
classes  of  policies  for  a  series  of  years,  one  is  enabled  to  judge 
pretty  correctly  of  their  relative  insurance  value. 

By  running  the  eye  over  these  tables,  it  will  be  noticed  that 
the  cost  of  insurance  in  a  whole  life  policy  increases  from  year 
to  year,  while  that  of  a  ten  payment  life  and  short  term  endow- 
ment decreases  until  we  get  among  the  older  ages.  The  reason 
of  this  that  the  tabular  cost  of  insurance  depends  upon  two  vari- 
able quantities  which  are  multiplied  into  each  other,  the  proba- 
bility of  dying  which  is  continually  increasing  and  the  amount 
at  risk  which  is  continually  decreasing.  If  the  amount  at  risk 
decreases  with  sufficient  rapidity,  as  in  a  ten  year  endowment, 
the  cost  of  insurance  is  annually  lessened,  until  the  last  year  it 
is  nothing.  In  a  twenty  year  endowment,  the  cost  of  insurance 
increases  or  decreases  each  successive  year?  according  to  the 
age  of  the  policy-holder  at  the  time  he  was  insured. 


OF  LIFE  INSURANCE, 


121 


TABLE  No.  XLII. 

COST  OF  INSURANCE  PER  $1,000  OF  AN  ORDINARY  LIFE  SINGLE-PRE- 
MIUM POLICY,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

Cost  of  Insurance. 

Age. 

Cost  of  Insurance. 

Age. 

Cost  of  Insurance. 

20 

6.11 

40 

6-55 

60 

11.83 

21 

6.12 

41 

6.61 

6l 

12.40 

22 

6.13 

42 

6.68 

62 

13.01 

23 

6.14 

43 

6.76 

63 

I3-65 

24 

6.14 

44 

6.86 

64 

14.32 

25 

6.15 

45 

6.96 

65 

I5-03 

26 

6.16 

46 

7.09 

66 

15-78 

27 

6.17 

47 

7.24 

67 

16.55 

28 

6.18 

48 

7.41      . 

68 

I7-36 

29 

6.20 

49 

7.62 

69' 

18.20 

30 

6.21 

50 

7.86 

70 

19.06 

31 

6.23 

5i 

8.12 

7i 

19-93 

32 

6-25 

52 

8.41 

72 

20.78 

33 

6.27 

53 

8-73 

73 

21.  60 

34 

6.30 

54 

9.08 

74 

22-39 

35 

6.32 

55 

9-45 

75 

23-I3 

36 

6.36 

56 

9.87 

37 

6.40 

57 

10.31 

38 

6.44 

58 

10.78 

39 

6.49 

59 

11.29 

TABLE  No.  XLII— (CONTINUED.) 

COST  OF  INSURANCE  PER  $1.000  OF  AN  ORDINARY  LIFE  SINGLE-PRE- 
MIUM POLICY,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

Cost  of  Insurance. 

Age. 

Cost  of  Insurance. 

Age. 

Cost  of  Insurance. 

20 

5-42 

40 

6.33 

60 

11.78 

21 

5-45 

41 

6.38 

6l 

12.27 

22 

5-48 

42 

6.44 

62 

12.78 

23 

5-5i 

43 

6-54 

63 

I3-32 

24 

5-54 

44 

6.68 

64 

13-87 

25 

5-58 

45 

6-85 

65 

H-45 

26 

S-63 

46 

7.07 

66 

15-05 

27 

5-65 

47 

7-30 

67 

*5-67 

28 

5-70 

48 

7-54 

68 

16.29 

29 

5-74 

49 

7.80 

69 

16.91 

3«> 

5-79        • 

50 

8.08 

70 

17-55 

31 

5-84 

5i 

8-37 

7i 

18.19 

32 

5-89 

52 

8.69 

72 

18.83 

33 

5-95 

53 

9.02 

73 

19.48 

34 

6.00 

54 

9-36 

74 

20.13 

35 

6.05 

55 

9.72 

75 

20.77 

36 

6.11 

56 

'     IO.II 

37 

6.16 

57 

10.49 

38 

6.22 

58 

10.89 

39 

6.27 

59 

11.32 

For  net  value  of  an  Ordinary  Life  Single-Premium  Policy,  see  Tables  No.  XVII I  and  XIX. 


122 


PRINCIPLES  AND  PRACTICE 
TABLE  No.  XLIIL 


COST  OF  INSURANCE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  DURING 
VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7-77 

7-78 

7-79 

7.80 

7.80 

7.81 

7.82 

7.84 

21 

7.82 

7-83 

7.84 

7-84 

7-85 

7-86 

7.87 

7-88 

22 

7.87 

7-87 

7.88 

7.89 

7.90 

7.91 

7.92 

7-94 

23 

7.92 

7.92 

7-93 

7-94 

7-95 

7.96 

7-98 

8.00 

24 

7-97 

7-97 

7-98 

S.oo 

8.01 

8-03 

8.04 

8.06 

25 

8.02 

8.03 

8.04 

8.t5 

8.07 

8.09 

8.10 

8.13 

26 

8.08 

8.09 

8.10 

8.12 

8.14 

8.I5 

8.18 

8.21 

27 

8.14 

8.15 

8.17 

8.19 

8.20 

8.23 

8.26 

8.29 

28 

8.21 

8.23 

8.24 

8.26 

8.28 

8.3I 

S-34 

8-37 

29 

8.28 

8.30 

8-32 

8-34 

8-37 

8.40 

8-43 

8.47 

30 

8.36 

8.38 

8.40 

8-43 

8.46 

8-49 

8-54 

S.s8 

31 

8.44 

.8.48 

S.so 

8-53 

S-s6 

8.60 

8.64 

8.71 

32 

8-53 

8.56 

8.60 

8.62 

8.67 

8.71 

8.78 

8.84 

33 

8.64 

8.67 

8.70 

8-75 

8-79 

8.85 

8.91 

8.99 

34 

8-75 

8.78 

8.82 

8.87 

8.92 

8-99 

9.07 

9-i5 

35 

8.86 

8.91 

8-95 

9.02 

9.08 

9.16 

9-23 

9-33 

36 

9.00 

9.04 

9.11 

9.17 

9-25 

9-32 

9.42 

9-52 

37 

9-i3 

9.20 

9.26 

9-34 

9.42 

9-52 

9.62 

9-75 

38 

9-3o 

9-36 

9-45 

9-52 

9.62 

9-73 

9.86 

10.00 

39 

9-47 

9-56 

9-63 

9-73 

9-84 

9-97 

10.12 

10.30 

40 

9.67 

9-75 

9-85 

9.96 

10.09 

10.24 

10.42 

10.63 

4i 

9.88 

9.98 

10.  08 

IO.22 

10.37 

10.56 

10.76 

II.OI 

42 

IO.II 

10.22 

10.36 

10.51 

10.70 

10.91 

ii.  16 

11.46 

43 

10.36 

lO.SI 

10.66 

10.85 

n.  06 

11.31 

11.62 

11.97 

44 

10.66 

I0.8l 

II.  OI 

11.22 

11.48 

11.79 

12.15 

12.54 

45 

10.98 

II.  IS 

11.40 

11.66 

11.98 

12.34 

12.74 

13.18 

46 

"•37 

"•59 

11.85 

12.  IS 

12.54 

12.95 

13-40 

13.89 

47 

11.79 

12.06 

12.39 

12.76 

i3-!7 

13-63 

14-13 

1468 

48 

12.28 

12.  6l 

12.99 

13-41 

13.88 

H-39 

H-95 

15-56 

49 

12.85 

13.24 

13-67 

14.14 

14.66 

15-23 

15-85 

16.53 

50 

I3-50 

J3-94 

14.42 

H-95 

15-54 

16.17 

16.86 

17-59 

5i 

14.23 

14.72 

15.26 

iS-86 

16.54 

17.21 

17.96 

18.75 

52 

15-05 

15.60 

16.21 

16.87 

I7-58 

18.35 

19.16 

20.04 

53 

15-95 

16.58 

17-25 

17.99 

18.77 

19.60 

20.50 

21.46 

54 

16.97 

17.66 

18.41 

19.22 

20.07 

20.99 

21-97 

23.01 

55 

18.10 

18.87 

19.69 

20.57 

21.51 

22.52 

23-59 

24.71 

56 

19.36 

20.20 

21.10 

22.07 

23.10 

24.20 

25-35 

26.56 

57 

20.75 

21.67 

22.67 

23-73 

24.85 

26.04 

27.28 

28.59 

58 

22.28 

23-3I 

24-39 

25-55 

26.77 

28.05 

29-39 

30.82 

59 

23-99 

25.11 

26.30 

27.56 

28.87 

30.26 

3i-73 

33-26 

60 

25-87 

27.10 

28.40 

29-75 

3i-i8  , 

32.69 

34-»7 

35-91 

OF  LIFE  INSURANCE. 


123 


TABLE  No.  XLIV. 

COST  OF  INSURANCE  PER  $1,000  OF  A  TEN-PAYMENT  LIFE   POLICY, 
DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

S'.cond 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

7.64 

7-52 

7-39 

7-25 

7.09 

6.92 

6-75 

6-57 

21 

7.70 

7-56 

7-43 

7.28 

7-12 

6-95 

6.78 

6.58 

22 

7-74 

7.60 

7.46 

7-31 

7.16 

6.99 

6.80 

6.61 

23 

7.78 

7-65 

7-50 

7-35 

7.19 

7.02 

6.83 

6.64 

24 

7-83 

7.69 

7-55 

7.40 

7-23 

7.06 

6.87 

6.66 

25 

7-88 

7-74 

7.60 

7-44 

7.27 

7.09 

6.90 

6.69 

26 

7-94 

7.80 

7-65 

7-49 

7-32 

7-i3 

6.94 

6-73 

27 

8.00 

7-85 

7.71 

7-54 

7-37 

7.18 

6.99 

6.77 

28 

8.06 

7.92 

7.76 

7.60 

7.42 

7.24 

7-03 

6.81 

29 

8.13 

7-99 

7-83 

7.66 

7.48 

7-29 

7.08 

6.86 

3° 

8.21 

8.05 

7.90 

7-73 

7-55 

7-35 

7-i5 

6.92 

31 

8.28 

8.13 

7.98 

7.81 

7.62 

7.42 

7.21 

6.99 

32 

8.37 

8.23 

8.06 

7.88 

7.70 

7-50 

7.29 

7.06 

33 

8.47 

8.32 

8.15 

7.98 

7-79 

7.60 

7-37 

7.14 

34 

8.57 

8.41 

8.26 

8.08 

7.90 

7.69 

7-47 

7-23 

35 

8.68 

8-53 

8-37 

8.20 

8.01 

7.81 

7-57 

7-33 

36 

8.81 

8.65 

8.50 

8.32 

8.14 

7-92 

7.69 

7-44 

37 

8.94 

8.80 

8.63 

8.47 

8.27 

8.06 

7.82 

7-57 

38 

9.10 

8-95 

8.80 

8.61 

8.42 

8.20 

7.98 

7.71 

39 

9.27 

9-i3 

8.96 

8.78 

8-59 

8.38 

8.14 

7.89 

40 

9.46 

9-3i 

9-T5 

8.97 

8.78 

8.57 

8-35 

8.09 

4i 

9.66 

9-51 

9-35 

9.19 

9.00 

8.80 

8-57 

8.32 

42 

9.88 

9-74 

9.60 

9-43 

9.26 

9.06 

8.84 

8-59 

43 

10.13 

10.00 

9.86 

9.71 

9-54 

9-36 

9-i5 

8.91 

44 

10.42 

10.29 

10.17 

10.03 

9.88 

9.71 

9-5i 

9.26 

45 

10.72 

10.63 

10.52 

10.40 

10.27 

IO.  12 

9.92 

9-65 

46 

11.09 

II.  OO 

10.92 

10.83 

10.70 

10-57 

10.37 

10.09 

47 

11.50 

"•45 

11.40 

n-33 

11.23 

II.08 

10.86 

10.57 

48 

11.98 

11.96 

11.94 

11.88 

11.79 

11.64 

11.42 

II.  IO 

49 

I2-53 

12.52 

12.54 

12.51 

12.42 

12.27 

12.03 

11.68 

5° 

13.16 

13.21 

13.22 

13.20 

I3-I3 

12-97 

12.71 

12.32 

51 

I3-87 

13-94 

13.98 

13.98 

13.90 

13-74 

13.46 

13.01 

52 

14.66 

14-70 

14.83 

14.83 

14.74 

H-59 

14.27 

13-77 

53 

'5-5.5 

15.68 

15-77 

15-79 

I5-72 

15-53 

15-  !7 

14.61 

54 

16.54 

16.70 

16.82 

16.85 

16.77 

16.56 

16.16 

15-5* 

55 

17.64 

17.84 

17.97 

17.94 

17.94 

17.70 

17.24 

16.50 

56 

18.86 

19.10 

19.25 

I9-3I 

19.22 

18.95 

18.43 

17-57 

57 

20.22 

20.48 

20.67 

20.74 

20.69 

20.33 

19.72 

'8-73 

58 

21.71 

22.03 

22.24 

22.32 

22.20 

21.83 

21.13 

2O.OI 

59 

23-38 

23-73 

23.92 

24.06 

23.92 

23-49 

22.70 

21.40 

60 

25.22 

25.62 

25.90 

25.07 

25.81 

25-33 

24.41 

22.91 

124 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XLV. 

COST  OF  INSURANCE  PER  $1,000  OF  A  TEN- YEAR  ENDOWMENT  POLICY, 
DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

Ninth 
year. 

20 

7.19 

6-59 

5-95 

5.26 

4-52 

3-73 

2.90 

2.OO 

1.03 

21 

7.24 

6.63 

5-99 

5-29 

4-55 

3-76 

2.92 

2.OI 

1.04 

22 

7.29 

6.68 

6.03 

5-33 

4-59 

3.80 

2-94 

2.03 

1.05 

23 

7-34 

6.72 

6.07 

5-37 

4-63 

3-83 

2.97 

2.05 

1.  06 

24 

7-38 

6-77 

6.12 

5-42 

4.67 

3-87 

3-00 

2.07 

1.08 

25 

7-43 

6.82 

6.17 

5-46 

4.71 

3-90 

3-03 

2.IO 

1.09 

26 

7-49 

6.88 

6.22 

5-52 

4.76 

3-94 

3-07 

2.13 

i.  ii 

27 

7-56 

6.94 

6.28 

5-57 

4.81 

3-99 

3-" 

2.15 

1.  12 

28 

7.62 

7.00 

6-34 

5-63 

4.86 

4.04 

3-i5 

2.18 

I.I4 

29 

7.69 

7.07 

6.41 

5-69 

4-93 

4.09 

3-i9 

2.22 

1.16 

30 

7-77 

7.14 

6.48 

5-77 

4-99 

4-15 

3-24 

2.26 

1.18 

31 

7-85 

7-23 

6.56 

5-84 

5.06 

4.22 

3-30 

2.30 

i.  20 

32 

7-93 

7-32 

6.65 

5-92 

5-H 

4.28 

3-36 

2-34 

1.23 

33 

8.04 

7.41 

6-74 

6.01 

5-22 

4-37 

3-42 

2-39 

1.26 

34 

8.14 

7-5i 

6.84 

6.ii 

5-32 

4-45 

3-50 

2-45 

1.29 

35 

8.25 

7-63 

6-95 

6.23 

5-42 

4-55 

3-58 

2.51 

1.32 

36 

8.38 

7-75 

7.09 

6-35 

5-54 

4-65 

3-67 

2.58 

1-36 

37 

8.51 

7.90 

7.22 

6-49 

5-66 

4.76 

3-76 

2-65 

1.41 

38 

8.68 

8.05 

7-38 

6.63 

5.81 

4-89 

3-88 

2.74 

1.46 

39 

8.84 

8.23 

7-54 

6-79 

5-96 

5-°4 

4.00 

2.84 

I-51 

40 

9.04 

8.41 

7-73 

6-97 

6.14 

5-i9 

4.14 

2-95 

1.58 

4i 

9-23 

8.61 

7-93 

7.18 

6-33 

5-38 

4-3i 

3.08 

1.66 

42 

9-45 

8.84 

8.16 

7.40 

6.56 

5-59 

4-49 

3-23 

i-75 

43 

9.70 

9.10 

8.42 

7.67 

6.81 

5-83 

4.71 

3-40 

1.84 

44 

9.99 

9-38 

8.72 

7.96 

7.10 

6.ii 

4.96 

3-59 

1.96 

45 

10.30 

9.72 

9-°5 

8.30 

7-44 

6-43 

5-24 

3.80 

2.08 

46 

10.66 

10.09 

9-44 

8.70 

7-83 

6.80 

5-55 

4.04 

2.22 

47 

11.07 

10.52 

9.89 

9.16 

8.27 

7.20 

5-9i 

4-32 

2.38 

48 

"•54 

1  1.  02 

10.41 

9.67 

8.76 

7-65 

6.29 

4.62 

2-55 

49 

12.09 

n-59 

10.99 

10.24 

9-3i 

8.16 

6-73 

4-96 

2-75 

50 

12.72 

12.24 

11.63 

10.87 

9-93 

8-73 

7-23 

5-33 

2.96 

5i 

13.42 

1295 

12.35 

"•59 

10.61 

9-36 

7-77 

5-75 

3-20 

52 

14.20 

13-75 

I3-I7 

12.39 

11.38 

10.07 

8.38 

6.22 

3-48 

53 

15.08 

14.66 

14.07 

13.28 

12.23 

io.S> 

9.06 

6-75 

3-78 

54 

16.06 

15-65 

15.08 

14.27 

13.18 

"•73 

9.82 

7-33 

4.12 

55 

I7-I5 

16.77 

16.19 

15-36 

14.23 

12.70 

10.66 

7-99 

4-50 

56 

18.37 

18.00 

17.42 

16.59 

15.40 

I3-78 

1  1.  60 

8.71 

4-92 

57 

19.72 

19-37 

18.80 

17.94 

16.71 

14.99 

12.64 

9-52 

5-40 

58 

21.20 

20.89 

20.33 

19-45 

18.16 

16.32 

13.80 

10.43 

5-93 

59 

22.86 

22.58 

22.03 

21.12 

19.76 

17.80 

15.11 

11.44 

6-53 

60 

24.69 

2445 

23.90 

22-97 

2i-53 

19.47 

16.56 

12.58 

7.20 

1 

i 

OF  LIFE   INSURANCE. 


TABLE  No.  XLVI. 

COST  OF  INSURANCE  PER$I,OOO  OF  A  FIFTEEN- YEAR  ENDOWMENT  POLICY, 
DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7-45 

7.12 

6.77 

6.40 

5-99 

5-56 

5.10 

4.6l 

21 

7-50 

7.17 

6.82 

6-44 

6.03 

5-61 

5-15 

4-65 

22 

7-55 

7-22 

6.86 

6.48 

6.08 

5-65 

5-^9 

4.70 

23 

7.60 

7.27 

6.91 

6-54 

6.13 

5-70 

5-24 

4-75 

24 

7-65 

7-3' 

6.97 

6-59 

6.19 

5-76 

S-29 

4-79 

25 

7.70 

7-37 

7.02 

6.65 

6.25 

5-8i 

5-35 

4-85 

26 

7.76 

7-43 

7.08 

6.71 

6-31 

5-87 

5-4i 

4.91 

27 

7-83 

7-50 

7-i5 

6.77 

6-37 

5-94 

5-48 

4.98 

28 

7.89 

7-57 

7.22 

6.84 

6.44 

6.02 

5-55 

5-04 

29 

7-97 

7.64 

7.29 

6.92 

6-53 

6.09 

5-62 

S-« 

3° 

8.05 

7.72 

7-38 

7.01 

6.61 

6.17 

5-71 

5-21 

31 

8.13 

7.81 

7-47 

7.10 

6.70 

6.27 

5.81 

5-3i 

32 

8.22 

7.91 

7-57 

7.20 

6.81 

6.38 

5-92 

5-4i 

33 

8.32 

8.01 

7.67 

7-3i 

6.92 

6.50 

6-03 

5-53 

34 

8-43 

8.12 

7-79 

7-43 

7-05 

6.62 

6.16 

5-65 

35 

8-54 

8.25 

7.91 

7-57 

7.18 

6.76 

6.30 

5-79 

36 

8.68 

8.38 

8.06 

7.71 

7-34 

6.91 

6-45 

5-94 

37 

8.82 

8-54 

8.22 

7.88 

7-50 

7.08 

6.62 

6**    *  • 
.12 

33 

8.98 

8.70 

8.40 

8.05 

7.68 

7.27 

6.82 

6.3I 

39 

9-15 

8.89 

8.58 

8.25 

7.88 

7-48 

7-03 

6-53 

40 

9-35 

9.08 

8.79 

8.46 

8.ii 

7.71 

7.28 

6.78 

4i 

9-55 

9-30 

9.01 

8.71 

8.36 

7-99 

7-56 

7-07 

42 

9-79 

9-54 

9.28 

8.98 

8.66 

8.29 

7.88 

7.41 

43 

10.04 

9.82 

9-57 

9-3° 

8-99 

8.64 

8.26 

7.80 

44 

10.34 

IO.I2 

9.91 

9-65 

9-37 

9.06 

8.68 

8.23 

45 

10.66 

10.48 

10.28 

10.06 

9.82 

9-53 

9.17 

8.71 

46 

11.04 

10.88 

10.72 

10.54 

10.35 

10.05 

9-70 

9.26 

47 

"•45 

"•34 

11.23 

11.08 

10.89 

10.64 

10.30 

9.87 

48 

11.94 

11.88 

ii.  81 

11.69 

"•53 

11.30 

10.98 

10.54 

49 

12.51 

12.49 

12.46 

12.38 

12.24 

12.04 

"•73 

11.30 

50 

I3-I5 

13.18 

13.18 

I3-H 

13.04 

12.86 

12.57 

12.14 

5i 

13.88 

13-95 

13-99 

13-99 

x3-93 

I3-78 

I3-50 

13-07 

52 

14.68 

14.81 

14.90 

14.94 

14.92 

14.79 

14-53 

14.11 

53 

I5-58 

15-77 

i5-9i 

16.00 

16.01 

I5-91 

,15.68 

1^.26 

54 

16.60 

16.83 

17.04 

17.17 

17.22 

17.17 

16.95 

16.54 

55 

17.72 

18.02 

18.28 

18.47 

iS-57 

18.55 

18.37 

17.96 

56 

18.97 

19-34 

19.65 

19.91 

20.07 

20.09 

19-93 

19-53 

57 

20.35 

20.79 

21.  18 

21.50 

21.72 

21.79 

21.66 

21.26 

58 

21.88 

22.40 

22.88 

23.27 

23-55 

23.67 

23-57 

23-3° 

59 

23-58 

24.19 

24-75 

25-23 

25-57 

25-74 

25.70 

25-35 

60 

25.46 

26.17 

26.82 

27-37 

27-79 

28.05 

28.05 

27.72 

126 


PRINCIPLES  AND  PRACTICE 


TABLE   No.  XLVII. 
COST  OF  INSURANCE  PER  $ i, ooo  OF  A  TWENTY- YEAR  ENDOWMENT  POLICY, 

DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Affe. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
)ear. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

7-58 

7-38 

7.17 

6-95 

6.70 

6.44 

6  17 

5-88 

21 

7.62 

7-43 

7.22 

6.99 

6-75 

6.50 

6.22 

5-93 

22 

7.67 

7.48 

7.27 

7.04 

6.80 

6-55 

6.27 

5-98 

23 

7.72 

7-53 

7-32 

7.IO 

6.86 

6.60 

6-33 

6.04 

24 

7-78 

7-58 

7-37 

7-15 

6.92 

6.67 

6.40 

6.  10 

25 

7-83 

7.64 

7-44 

7.21 

6.98 

6-73 

6.46 

6.17 

26 

7.89 

7.70 

7-50 

7-28 

7-05 

6.80 

6-53 

6.25 

27 

7.96 

7-77 

7-57 

7-36 

7.12 

6.88 

6.62 

6-33 

28 

8.02 

7-84 

7.64 

7-43 

7.20 

6.96 

6.70 

6.42 

29 

8.10 

7.92 

7.72 

7-5i 

7.29 

7-05 

6.79 

6.52 

30 

8.18 

8.00 

7.81 

7.61 

7-39 

7-i5 

6.90 

6.62 

31 

8.26 

8.09 

7.91 

7.71 

7.48 

7.26 

7.01 

6-75 

32 

8-35 

8.19 

8.01 

7.8! 

7.60 

7-38 

7.14 

6.87 

33 

8.46 

8.30 

8.ii 

7-93 

7.72 

7-5i 

7.27 

7-C2 

34 

8-57 

8.40 

8.24 

8.06 

7.87 

7-65 

7-43 

7.17 

35 

8.68 

8.1:4 

8-37 

8.21 

8.02 

7-82 

7-59 

7-35 

36 

8.82 

8.67 

8-53 

8.36 

8.19 

7-99 

7.78 

7-54 

37 

8.96 

8.84 

8.69 

8.c4 

8.37 

8.18 

7-97 

7.76 

38 

9-*3 

9.00 

8.88 

8.72 

8.57 

8-39 

8.21 

7-99 

39 

9-30 

9.20 

9.07 

8.94 

8.79 

8.64 

8.46 

8.28 

40 

9-5° 

9-39 

9-29 

9.16 

9.04 

8.90 

8-75 

8.56 

4i 

9.71 

9.62 

9-52 

9-43 

9-32 

9.21 

9.08 

8-94 

42 

9-94 

9.87 

9.80 

9.72 

9.64 

9-55 

9.46 

9-36 

43 

10.20 

10.16 

10.10 

10.06 

IO.OO 

9-95 

9.90 

9.84 

44 

10.50 

10.47 

10.46 

10.42 

10.42 

10.42 

10.41 

10.38 

45 

IO.82 

10.84 

10.85 

10.87 

10.91 

10.95 

10.97 

10.97 

46 

II.  21 

11.24 

11.30 

11.38 

11.46 

"•54 

n.  60 

11.64 

47 

11.63 

11.72 

11.83 

11.96 

12.09 

12.21 

12.31 

12.39 

48 

12.12 

12.27 

12.44 

12.  6l 

12.78 

12.94 

13.10 

13.21 

49 

12.69 

12.90 

13.11 

13-34 

13-55 

13-77 

13-97 

14.14 

50 

13-34 

13.60 

I3-87 

14.14 

14.42 

14.69 

14.94 

i«;.i6 

5i 

14.08 

H-39 

14.71 

15-05 

15-38 

i<c.7i 

16.02 

16.26 

52 

14.89 

15.26 

15.66 

16.05 

16.45 

16.84 

17.20 

17-53 

53 

15.80 

16.25 

16.70 

17.17 

17.64 

18.08 

18.52 

18.91 

54 

16.82 

17-33 

17.86 

18.40 

18.93 

19.47 

19.97 

20.43 

55 

17-95 

18.55 

i9-'5 

19.16 

20.38 

20.99 

21.58 

22.11 

56 

19.22 

19.88 

20.56 

21.27 

21.97 

22.67 

23-34 

23-95 

57 

20.61 

21.36 

22.14 

22.93 

23-74 

24-53 

25.28 

25.98 

58 

22.15 

23.00 

23.88 

24.78 

25.68 

26.56 

27.41 

28.23 

59 

23.86 

24.81 

25.80 

26.80 

27.80 

28.79 

29.78 

30.69 

60 

25-75 

26.82 

27.91 

29.02 

30.14 

31.27 

32-37 

33-40 

OF  LIFE  INSURANCE.  I27 

TABLE  No.  XLVIII. 

COST  OF  INSURANCE  PER  $1,000  OF  A  TWENTY-FIVE  YEAR  ENDOWMENT 
POLICY,  DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


4r<. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

7.65 

7-33 

7.40 

7.26 

7.II 

6-95 

6.78 

6.60 

21 

7.70 

7-58 

7-45 

7-31 

7.16 

7.00 

6.84 

6.65 

22 

7-75 

7-63 

7-50 

7-36 

7-21 

7.06 

6.89 

6.72 

23 

7.80 

7.68 

7-55 

7.42 

7.27 

7.12 

6.96 

6.78 

24 

7-85 

7-73 

7.61 

7.48 

7-33 

7.18 

7.02 

6.85 

25 

7.90 

7-79 

7.67 

7-54 

7.40 

7-25 

7.09 

6.92 

26 

7.96 

7-85 

7-73 

7.61 

7-47 

7-33 

7.17 

7-01 

27 

8.03 

7.92 

7.81 

7.68 

7-55 

7.41 

7.26 

7-IO 

28 

8.10 

7-99 

7.88 

7-76 

7-63 

7-50 

7-36 

7.19 

29 

8.17 

8.07 

7.96 

7-85 

7-73 

7.60 

7-45 

7-31 

3° 

8.25 

8.15 

8.05 

7-94 

7-83 

7.69 

7-57 

7.42 

31 

8-34 

8.24 

8.15 

8.05 

7-93 

7.81 

7.68 

7-56 

32 

8-43 

8-35 

8.26 

8.15 

S.os 

7-94 

7-83 

7.70 

33 

8-54 

8.46 

8.36 

8.28 

8.18 

S.oS 

7-97 

7-86 

34 

8.65 

8.56 

8-49 

8.41 

8-33 

8.23 

8.14 

8.03 

35 

8.76 

8.70 

8.63 

8.56 

8.48 

8.41 

8.31 

8.22 

36 

8.90 

8.84 

8.79 

8.72 

8.66 

S.sS 

8-51 

8.42 

37 

9.04 

9.00 

8-95 

8.90 

8.84 

8.79 

8.72 

8.66 

33 

9.21 

9.17 

9.14 

9.09 

9-05 

9.01 

8.96 

8.92 

39 

9-38 

9-36 

9-33 

9-3i 

9.28 

9.26 

9.24 

9-23 

40 

9-58 

9-56 

9-56 

9-54 

9-55 

9-54 

9-55 

9-56 

41 

9-79 

9-79 

9.80 

9.82 

983 

9-87 

9-9° 

9-95 

42 

10.03 

10.04 

10.08 

IO.  II 

10.17 

10.23 

10.30 

10.41 

43 

10.28 

iQ-33 

10.38 

10.46 

10.54 

10.64 

10.78 

10.92 

44 

10.58 

10.65 

10.74 

10.84 

10.97 

11.13 

11.31 

11.50 

45 

10.91 

11.02 

11.14 

11.29 

11.48 

11.69 

11.91 

12.14 

46 

11.29 

"•43 

1  1.  60 

ii.Si 

12.05 

12.31 

12.58 

12.89 

47 

11.72 

11.91 

12.14 

12.40 

12.69 

13.00 

I3-32 

13.66 

48 

12.24 

12.46 

12.75 

13.07 

13.40 

I3-76 

14.18 

14-54 

49 

12.78 

I3-I3 

13-44 

13.80 

14.20 

14.62 

15.09 

15-53 

50 

13-44 

13-80 

14.20 

14.63 

15.09 

15-57 

16.09 

16.61 

5i 

14.17 

H-59 

15-05 

15-55 

16.07 

16.63 

17.21 

17.79 

52 

14.99 

15-47 

16.00 

16.56 

17.16 

17.79 

18.43 

19.11 

53 

15.90 

16.46 

17.06 

17.70 

iS-37 

19.06 

19.80 

20.55 

54 

16.92 

17-55 

18.23 

18.94 

19.69 

20.48 

21.30 

22.14 

55 

18.05 

18.77 

19.52 

20.30 

21.15 

22.03 

22.95 

23.89 

56 

19.32 

20.  ii 

20.94 

21.83 

22.77 

23-74 

24-75 

25-79 

57 

20.71 

21-59 

22.52 

23-51 

24-54 

25.62 

26.73 

27.87 

58 

22.25 

23-23 

24.26 

25-35 

26.49 

27.67 

28.89 

30.16 

59 

23.96 

25-04 

26.19 

27.38 

28.62 

29.92 

31.28 

32.66 

60 

25-85 

27.04 

28.30 

29.60 

30.96 

32.40 

33-88 

35-39 

i 

128 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  XLIX. 

COST  OF  INSURANCE  PER  $1,000  OF  A  THIRTY- YEAR  ENDOWMENT  POLICY, 
DURING  VARIOUS  YEARS,  AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

20 

7.69 

7.62 

7-54 

7.46 

7-36 

7.26 

7.16 

7-05 

21 

7-74 

7.67 

7-59 

7-50 

7.41 

7-32 

7.22 

7-10 

22 

7-79 

7.72 

7.64 

7-55 

7-47 

7-37 

7.27 

7.17 

23 

7.84 

7-77 

7-69 

7.61 

7-53 

7-44 

7-34 

7.24 

24 

7.89 

7-82 

7-75 

7.67 

7-59 

7*1 

7.41 

7-31 

25 

7-95 

7.88 

7.81 

7-74 

7.66 

7.58 

7.48 

7-39 

26 

8.01 

7-95 

7.88 

7.81 

7-73 

7-65 

7-57 

7-48 

27 

8.07 

8.01 

7-95 

7.89 

7-81 

7-73 

7.66 

7-57 

28 

8.14 

8.09 

8.03 

7-96 

7.90 

7-83 

7.76 

7.67 

29 

8.22 

8.17 

8.ii 

8-05 

7-99 

7-93 

7-85 

7-79 

30 

8.30 

8.25 

8.20 

8.15 

8.09 

8.02 

7-97 

7.91 

31 

8.38 

8-34 

8-30 

8.25 

8.20 

8-15 

8.09 

8.05 

32 

8.48 

8-44 

8.40 

8.36 

8.32 

8.27 

8.24 

8.19 

33 

8-58 

8-55 

8.51 

8.48 

8-45 

8.42 

8-39 

8.36 

34 

8.69 

8.66 

8.64 

8.62 

8.60 

8.58 

8.56 

8-53 

35 

8.81 

&8o 

8.78 

8.77 

8.76 

8-75 

8-74 

8-73 

36 

8.94 

8-93 

8-94 

8-93 

8-94 

8-93 

8-94 

8-94 

37 

9.09 

9.10 

9.10 

9.12 

9.12 

9.14 

9-*5 

9.19 

38 

9-25 

9.27 

9.29 

9-3i 

9-33 

9-37 

9.41 

9-45 

39 

9-43 

9.46 

9-49 

9-52 

9-56 

9.62 

9.68 

9-77 

40 

9-63 

9.66 

9.71 

9.76 

9-83 

9.90 

10.00 

IO.  II 

4i 

9.84 

9.89 

9-95 

10.03 

IO.  II 

10.23 

10.36 

10.51 

42 

10.07 

10.14 

10.23 

10.33 

10.46 

1  0.60 

10.77 

10.98 

43 

10.33 

10.43 

!o-53 

10.63 

10.83 

1  1.  02 

11.25 

11.51 

44 

10.63 

10.74 

10.90 

ii.  06 

11.26 

11.51 

"•79 

12.10 

45 

10.95 

II.  12 

11.29 

11.51 

11.77 

12.  IO 

12.40 

12-75 

46 

".-34 

11.52 

"•75 

12.03 

12-35 

12.69 

13-07 

I3.48 

47 

11.76 

12.00 

12.29 

12.62 

12.99 

13-39 

13.82 

14.29 

48 

12.25 

12.56 

12.90 

13.29 

i3-7i 

14.16 

14.66 

«5-l9 

49 

12.83 

I3-I9 

13-59 

14.03 

14.50 

15.02 

I5-58 

16.18 

50 

I3-48 

13.90 

M-35 

14-85 

J5-39 

15.98 

16.61 

17.27 

5i 

14.21 

14.68 

15.20 

15-77 

'6-37 

I7-03 

17-73 

18.46 

53 

15-03 

I5-56 

16.15 

16.78 

17-47 

I8.I9 

18.96 

19.78 

53 

15-94 

16.55 

17.20 

17.91 

18.66 

19.46 

20.32 

21.22 

54 

16.96 

17.64 

18-37 

'9-J5 

19.98 

20.87 

21.  Si 

22.81 

55 

18.09 

18.85 

19.66 

20.51 

21.44 

22.42 

23-45 

24-54 

" 

OF  LIFE  INSURANCE. 


129 


TABLE  No.  L. 

COST  OF  INSURANCE  PER  $1,000  OF  AN  ORDINARY  LIFE  POLICY,  DURING 
VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth  * 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7-25 

7.28 

7-32 

7-37 

7.41 

7.46 

7-51 

7.56 

21 

7-33 

7-37 

7.41 

7.46 

7-50 

7-55 

7.60 

7-66 

22 

7.4i 

7.46 

7-51 

7-55 

7.60 

7-65 

7.71 

7-77 

23 

7-5i 

7-56 

7.60 

7-65 

7.71 

7-77 

7-83 

7-89 

24 

7.61 

7.66 

7.71 

7.76 

7.82 

7.88 

7-95 

8.02 

25 

7.71 

7.76 

7.82 

7.88 

7-94 

8.01 

8.08 

8.15 

26 

7.82 

7.88 

7-94 

8.00 

8.07 

8.14 

8.21 

8.29 

27 

7-94 

8.00 

8.06 

8.13 

8.20 

8.28 

8-35 

8.42 

28 

8.07 

8.13 

8.20 

8.27 

8-35 

8.42 

8.49 

8.57 

29 

8.20 

8.27 

8-34 

8.42 

8.49 

8-57 

8.65 

8-73 

3° 

8-35 

8.41 

8-49 

8.57 

8.64 

8.72 

8.80 

8.88 

31 

8.50 

8-57 

8.65 

8.73 

8.81 

8.89 

8.96 

9.04 

32 

8.66 

8.74 

8.81 

8.89 

8.97 

9-05 

9-13 

9.21 

33 

8.83 

8.90 

8.98 

9.07 

9.14 

9-23 

9-3i 

9-38 

34 

9.00 

9.08 

9.16 

9.24 

9-33 

9.40 

9.48 

9-56 

35 

9.18 

9.26 

9-34 

9-43 

9-5i 

9-58 

9.67 

9-77 

36 

9-37 

9-45 

9-54 

9.62 

9.70 

9.78 

9.88 

10.04 

37 

9-56 

9-65 

9-74 

9.81 

9.90 

10.00 

10.  16 

10.38 

38 

9.78 

9.86 

9-94 

10.03 

10.13 

10.29 

10.51 

10.78 

39 

9.99 

10.07 

10.16 

10.27 

10.43 

10.65 

10.92 

11.27 

40 

IO.2I 

10.30 

19.41 

'0-57 

10.80 

11.07 

11.42 

11.79 

41 

10-45 

10.56 

10.72 

10.96 

11.23 

"•59 

11.97 

12.37 

42 

10.72 

10.89 

11.13 

11.41 

11.77 

12.15 

12.56 

12.99 

43 

11.07 

11.30 

n-59 

11.96 

12-34 

12.76 

13.20 

13.66 

44 

11.50 

11.79 

12.  16 

12.55 

12.97 

13.42 

13.90 

14.40 

45 

11.99 

12.37 

12.77 

13.20 

i3-65 

14.14 

14.65 

15.20 

46 

12.60 

13.01 

13-44 

13.90 

14.40 

14.92 

15.48 

16.08 

47 

13.26 

13  7<> 

14.17 

14.67 

15.21 

I5-78 

16.38 

17.00 

48 

13-97 

H-45 

14.96 

15.51 

16.09 

16.71 

17-33 

18.01 

49 

14-75 

15-27 

15-83 

16.42 

i7-°5 

17.69 

18.38 

19.10 

50 

15-59 

16.16 

16.77 

17.41 

18.06 

18.77 

19.50 

20.24 

5' 

16.52 

17.14 

17.80 

18.46 

19.18 

*9-93 

20.69 

21.49 

52 

17-53 

18.20 

18.88 

19.62 

20.40 

2I.1O 

21.98 

22.83 

53 

18.64 

1933 

20.09 

20.87 

21.66 

22.50 

23-38 

24-34 

54 

19.81 

20.60 

21-39 

22.19 

23.06 

23-95 

24.94 

25.-97 

55 

21.  II 

21.93 

22.76 

23-54 

24.56 

25-58 

26.63 

27-75 

56 

22.51 

23-36 

24.26 

25.21 

26.25 

27-33 

28.48 

29.67 

57 

24.OO 

24-93 

25.90 

26.97 

28.08 

29.26 

30.48 

31-75 

58 

25-64 

26.63 

27-73 

28.88 

30-09 

31-34 

32-65 

34.02 

59 

27.42 

28.55 

29.72 

30.99 

32.26 

33-6i 

35-02 

36.46 

60 

29.41 

30.62 

31.92 

33-24 

34-63 

36.08 

37-57 

39-" 

61 

3I-58 

32-92 

34.28 

35-72 

37-22 

38.75 

40-34 

41.94 

'62 

33-98 

35-39 

36.88 

38.42 

40.00 

41-65 

43-40 

44-95 

63 

36.58 

38.11 

30-71 

41-34 

43-04 

44-75 

46.46 

48.21 

64 

39-43 

41.08 

42.76 

44-52 

46.29 

48.06 

49.87 

51.69 

65 

42-53 

44.28 

46.10 

47-93 

49-76 

51.64 

53-52 

55-42 

130 


PRINCIPLES  AND  PRACTICE 


TABLE   No.   LI. 

COST  OF  INSURANCE  PER  $1,000  OF  A  TEN- PAYMENT  LIFE  POLICY,  DURING 
VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Afft. 

first 
year. 

Second 
year. 

Third 
year. 

Fourth 

year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 

year. 

20 

7.II 

7.OO 

6.88 

6.76 

6.62 

6.47 

6.31 

6.14 

21 

7.19 

7.08 

6.96 

6.83 

6.69 

6-54 

6-37 

6.  20 

22 

7.27 

7.16 

7.04 

6.91 

6-77 

6.61 

6-44 

6.26 

23 

7-36 

7-25 

7.12 

6.99 

6.84 

6.69 

6.51 

6-33 

24 

7.46 

7-34 

7.22 

7.08 

6.94 

6-77 

6-59 

6.40 

25 

7-56 

7-44 

7-3i 

7.17 

7-02 

6.86 

6.67 

6-47 

26 

7-66 

7-54 

7.42 

7.27 

7.12 

6-95 

6.76 

6-55 

27 

7-77 

7.66 

7-52 

7-38 

7-22 

7-°5 

6.85 

663 

28 

7.90 

7-77 

7.64 

7-49 

7-33 

7-i5 

6-94 

6.71 

29 

8.03 

7.90 

7.76 

7.61 

7-44 

7-25 

7-03 

6-79 

30 

8.16 

8.04 

7.90 

7-74 

7-55 

7-36 

7-13 

6.87 

31 

8.31 

8.18 

8.03 

7.86 

7.68 

7-47 

7-23 

6.96 

32 

8.46 

8-33 

8.17 

8.00 

7.80 

7-58 

7-33 

7-05 

33 

8.62 

8.48 

8.32 

8.14 

7-93 

7.70 

7-43 

7-i3 

34 

8.79 

8.64 

8.47 

8.28 

8.07 

7-82 

7-54 

7-23 

35 

8.96 

8.8j 

8.63 

8-43 

8.20 

7-94 

7-65 

7-34 

36 

9-'5 

8.98 

880 

8.^9 

8-34 

8.07 

7.78 

7-49 

37 

9-38 

9.17 

8-97 

874 

8-49 

8.22 

7.96 

7-69 

3« 

9-54 

9-36 

9-i5 

8.92 

8.67 

8-43 

8.19 

7-93 

39 

9-74 

9-55 

9-34 

9.11 

8.90 

8.69 

8.46 

8.23 

40 

9-95 

9.76 

9-55 

9-36 

9.19 

8.99 

8.81 

8-55 

4i 

10.19 

IO.OO 

9-83 

9-68 

9-53 

9-38 

9.17 

8.89 

42 

10.45 

10.30 

10.19 

10.06 

9-95 

9-79 

9-56 

9.26 

43 

10.78 

10.69 

10.60 

10.52 

10.41 

10.23 

9-99 

9-6? 

44 

11.19 

11.13 

II.  IO 

11.03 

10.90 

10.72 

10.45 

10.10 

45 

11.67 

11.68 

11.65 

"•57 

11.44 

11.24 

10.95 

10.57 

46 

12.27 

12.27 

12.24 

12.  16 

1  2.  02 

ii.  81 

11.50 

11.07 

47 

12.90 

12.91 

12.89 

12.  8l 

12.66 

12.43 

12.09 

1  1.  60 

48 

13-59 

13.61 

13-59 

13-51 

13-36 

13.10 

12.71 

12.  IS 

49 

14-34 

14.38 

14-36 

14.28 

14.11 

13.82 

13-39 

12.80 

50 

if.i6 

15.21 

15.20 

15.12 

14.91 

14.60 

14.12 

!3-44 

5i 

16.05 

16.12 

16.12 

16.01 

15.80 

15-44 

14.89 

»4-l3 

52 

17.04 

17.11 

17.09 

16.99 

16.75 

16.33 

15-72 

14.88 

53 

18.11 

18.17 

18.17 

18.05 

17.76 

i7-3o 

16.63 

I5-72 

54 

19.25 

19-34 

19-33 

19.17 

18.86 

18.35 

17.64 

16.61 

55 

20.  5  1 

20.  6  1 

20.56 

20.40 

20.05 

19-53 

18.73 

17-59 

56 

21.87 

21.95 

21.92 

21-73 

21.40 

20.81 

19-93 

18.64 

57 

23-32 

23.42 

23-39 

23.24 

22.86 

22.22 

21.22 

19.79 

58 

24.91 

25-03 

25-05 

24.87 

24.47 

23-75 

22.U4 

21.  02 

59 

26.65 

26.83 

26.85 

26.68 

26.22 

25-42 

24.17 

22.34 

60 

28.60 

28.80 

28.84 

28.64 

28.14 

27.24 

25.84 

23-79 

OF  LIFE  INSURANCE.  jj, 

TABLE  No.  LII. 
Cos/-  OF  INSURANCE  PER  $1,000  OF  A  TEN-YEAR  ENDOWMENT  POLICY, 

DURING  VARIOUS    YEARS,   COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

6.70 

6.16 

5-58 

4-95 

4.28 

3-55 

2.76 

1*1 

.21 

6.78 

6.24 

5-65 

5-02 

4-34 

3.60 

2.8o 

1.94 

22 

6.86 

6.32 

5-73 

5-o8 

4.40 

3-66 

2-85 

1.98 

23 

6.96 

6.40 

5-8i 

5-i6 

4-47 

3-72 

2.90 

2.O2 

24 

7-05 

6.49 

5-89 

5-24 

4-54 

3-78 

2.96 

2.05 

25 

7.14 

6-59 

5-98 

5-33 

4.62 

3-85 

3-oi 

2.09 

26 

7-25 

6.69 

6.08 

5-42 

4.71 

3-92 

3-o7 

2.14 

27 

7-36 

6.80 

6.19 

5-52 

4-79 

4.00 

3-i3 

2.18 

28 

7-49 

6.92 

6.30 

5-62 

4.89 

4.08 

3-i9 

2.22 

29 

7.61 

7.04 

6.41 

5-73 

4-99 

4.16 

3.26 

2.28 

3° 

7-75 

7.17 

6-54 

5-85 

5-09 

4-25 

3-34 

2-33 

31 

7.89 

7-3i 

6.67 

5-97 

5-20 

4-35 

3-4i 

2.38 

32 

8.05 

7.46 

6.80 

6.09 

5-3i 

4.40 

3-49 

2-44 

33 

8.21 

7.60 

6-95 

6.22 

5-42 

4-54 

3-57 

2-49 

34 

8-37 

7-77 

7.10 

6.36 

5-55 

4-65 

3-65 

2-55 

35 

8.55 

7-93 

7-25 

6.51 

5-68 

4.76 

3-74 

2.63 

36 

8-73 

8.10 

7.42 

6.65 

5-8i 

4.87 

3-84 

2.71 

37 

8.91 

8.29 

7-59 

6.81 

5-95 

5-oo 

3-96 

2.82 

38 

9.12 

8.48 

7.76 

6.97 

6.ii 

5-17 

4-i3 

2-95 

39 

9-32 

8.67 

7-95 

7.16 

6.31 

5-38 

4-3i 

3.10 

40 

9-54 

8.88 

8.16 

7.40 

6.56 

5.62 

4-55 

3-27 

4i 

9-77 

9.12 

8-43 

7.69 

6-85 

5-9i 

4-79 

3-45 

42 

10.03 

9-42 

8-77 

8.03 

7.21 

6.23 

5-05 

3-66 

43 

10.36 

9-79 

9-^5 

8-45 

7.60 

6.58 

5-34 

3-88 

44 

10.77 

10.22 

9-63 

8.90 

8.02 

6-95 

5-67. 

4.12 

45 

11.24 

10-75 

10.14 

9.40 

8.48 

7-37 

6.02 

4-38 

46 

11.82 

11.32 

10.71 

9-94 

8-99 

7-83 

6.41 

4.67 

47 

12.24 

"•95 

11.32 

10.52 

9-54 

8-33 

6.83 

4-99 

48 

i3-i3 

12.63 

11.98 

11.17 

10.15 

8.88 

7.28 

5-33 

49 

13-87 

13-37 

12.71 

11.88 

10.81 

9.46 

7.80 

5-7i 

50 

14.69 

14.18 

13-52 

12.65 

"•53 

IO.I2 

8.36 

6.12 

5i 

15-57 

15-07 

H-39 

13.48 

12.32 

10.83 

8.94 

6-57 

52 

16.55 

16.04 

15-33 

14.40 

I3-I7 

11.58 

9-58 

7.06 

53 

17.61 

17.08 

16.36 

15-39 

14.09 

12.42 

10.29 

7.62 

54 

18.74 

18.23 

17.49 

16.45 

15.10 

13-34 

II.  IO 

8.27 

55 

19.99 

19.47 

18.69 

17.62 

16.20 

H-37 

11.98 

8.92 

56 

21-34 

20.80 

20.00 

18.90 

17-45 

i5-5i 

12.97 

9.67 

57 

22.79 

22.25 

21.44 

20.34 

18.88 

16.76 

14.04 

10.50 

58 

24.38 

23-84 

23.06 

21.92 

20.32 

18.14 

15-23 

11.42 

59 

26.10 

25-63 

24-83 

23.66 

21-97 

19.66 

16.55 

12.42 

60 

28.15 

27.58 

26.79 

2S-S6 

23.80 

21.34 

17.99 

'3-55 

132 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LIII. 
COST  OF  INSURANCE  PER  $i  ,000  OF  A  FIFTEEN-YEAR  ENDOWMENT  POLICY, 

DURING  VARIOUS  YEARS,    COMBINED    EXPERIENCE,  4  PER  CENT. 


AS*. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 

year. 

Eighth 
year. 

20 

6.94 

6.66 

6-35 

6.03 

5-67 

5-29 

4.88 

4-43 

21 

7-03 

6-74 

6.44 

6.H 

5-75 

5-37 

4-95 

4-50 

22 

7.II 

6.83 

6.52 

6.19 

5-84 

5-45 

5-03 

4-57 

23 

7.21 

6.92 

6.61 

6.29 

5-93 

5-54 

5-n 

4.66 

24 

7-3° 

7.02 

6.71 

6.38 

6.03 

5-63 

5-21 

4-75 

25 

7.40 

7.12 

6.82 

6.49 

6.13 

5-74 

5-3i 

4.84 

26 

7-5i 

7-23 

6-93 

6.60 

6.24 

5-84 

5-42 

4-94 

27 

7-63 

7-35 

7-05 

6.72 

6-35 

5-96 

5-53 

5-03 

28 

7-75 

7.48 

7.17 

6.84 

6.48 

6.08 

5-64 

5-H 

29 

7.88 

7.61 

7-3i 

6.98 

6.61 

6.20 

5-75 

5-27 

30 

8.03 

7-75 

7-45 

7.12 

6.74 

6.33 

5-88 

5-38 

31 

8.17 

7.90 

7.60 

7-25 

6.89 

6.47 

5-99 

5-50 

32 

8-33 

8.06 

7-75 

7.41 

7-°3 

6.61 

6.14 

5-63 

33 

8.50 

8.22 

7.91 

7-57 

7.19 

6.76 

6.29 

5-76 

34 

8.67 

8-39 

8.08 

7-73 

7-35 

6.92 

6-43 

5-9° 

35 

8.85 

8-57 

8.26 

7.91 

7-52 

7.08 

6-59 

6.06 

36 

9.04 

8-75 

8-44 

8.09 

7.69 

7-25 

6.76 

6.25 

37 

9-23 

8-95 

8.64 

8.27 

7.87 

7-44 

6.98 

6.51 

33 

9-44 

9.16 

8.83 

8-47 

8.08 

7.68 

7.26 

6.80 

39 

9-65 

9-36 

9.04 

8.70 

8-35 

7-99 

7-58 

7.14 

40 

9.87 

9-59 

9.28 

8.98 

8.68 

8-34 

7-97 

7-52 

4i 

IO.  II 

9.82 

9-59 

9-34 

9.06 

8-77 

8.40 

7-94 

42 

10.38 

10.  16 

9.96 

9-75 

9-52 

9-23 

8.87 

8-39 

43 

10.72 

10.57 

10.40 

10.25 

10.03 

9-45 

9-37 

8.89 

44 

11.15 

11.03 

10.94 

10.79 

10.59 

10.30 

9.92 

9-44 

45 

11.63 

n.  60 

11.52 

"•39 

11.19 

10.91 

10.53 

10.04 

46 

12.23 

12.21 

12.15 

12.03 

11.85 

11.58 

11.20 

10.70 

47 

12.88 

12.89 

12.84 

12.74 

12.57 

12.30 

"•93 

11.40 

43 

13-59 

I3.6l 

13-59 

i3-5i 

I3-36 

13.10 

12.71 

12.18 

49 

H-35 

14.41 

14.41 

14.36 

14.22 

13.96 

13-57 

13-03 

50 

!5-i9 

15.28 

I5-3I 

15.28 

I5-H 

14.90 

H-Si 

13-94 

5i 

16.10 

16.23 

16.30 

16.27 

16.16 

15-93 

I5-5I 

14.92 

52 

17.11 

17.27 

17-35 

I7-36 

17.27 

17.02 

16.61 

16.00 

53 

18.20 

lS-37 

18.51 

18.54 

18.44 

18.22 

17.82 

17-23 

54 

19.36 

19.60 

19.76 

19.80 

19-74 

19-53 

19.18 

18.58 

55 

20.65 

20-93 

21    10 

21.  18 

21.15 

2I.OO 

20.64 

20.05 

56 

22.05 

22-34 

22.56 

22.69 

22.73 

22  6l 

22.28 

21.67 

57 

23-53 

23.88 

24.16 

24-38 

24.46 

24.38 

24.06 

23.46 

58 

25-15 

25-57 

25-95 

26.23 

26.37 

26.31 

26.02 

25.42 

59 

26.93 

27.46 

27.89 

28.26 

28.45 

28.44 

28.18 

27-55 

f 

60 

28.99 

29-53 

30.07 

30.48 

30-73 

30.78 

30-52 

29.91 

OF  LIFE  INSURANCE. 


'33 


TABLE  No.  LIV. 

COST  OF  INSURANCE  PER  $I,OOOOF  A  TWENTY- YEAR  ENDOWMENT  POLICY, 
DURING  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Agt. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7.06 

6.90 

6-73 

6-55 

6-35 

6.13 

5-80 

5-65 

21 

7.14 

6.98 

6.82 

6.64 

6-43 

6.22 

5-99 

5-74 

22 

7-23 

7.08 

6.91 

6-73 

6-53 

6.32 

6.09 

5-84 

23 

7-33 

7.17 

7.00 

6.83 

6.63 

6.42 

6.19 

5-95 

24 

7-43 

7.27 

7.11 

6-93 

6.74 

6-53 

6.31 

6.05 

25 

7-53 

7-38 

7.22 

7-°5 

6.86 

6.65 

6.42 

6.17 

26 

7.64 

7-49 

7-34 

7.17 

6.98 

6.77 

6-55 

6.29 

27 

7-75 

7.62 

7.46 

7-30 

7.11 

6.91 

6.68 

6.42 

28 

7.88 

7-74 

7.60 

7-43 

7-25 

7.04 

6.81 

6.56 

29 

8.02 

7.89 

7-74 

7-57 

7-39 

7.18 

6.96 

6.70 

30 

8.16 

8.03 

7.89 

7-73 

7-54 

7-34 

7.11 

6.84 

31 

8.31 

8.19 

8.04 

7.88 

7.70 

7-49 

7.26 

7.00 

32 

8.47 

8-35 

8.20 

8.05 

7-S6 

7-65 

7.42 

7.16 

33 

8.64 

8.51 

8.38 

8.22 

8.03 

7-83 

7-59 

7-32 

34 

8.81 

8.69 

8-55 

8-39 

8.21 

8.00 

7-77 

7-50 

35 

9.00 

8.88 

8-73 

8.58 

8.40 

8.18 

7-94 

7.69 

36 

9.19 

9.06 

S-93 

8.77 

8.58 

8.38 

8.18 

7-92 

37 

9-38 

9.27 

9-i3 

8.97 

8-79 

8.60 

8.42 

8.25 

38 

9-59 

9.48 

9-34 

9.18 

9.02 

8.87 

8-75 

8.61 

39 

9.81 

9.69 

9-56 

9.42 

9-3i 

9.22 

9.12 

9.04 

40 

10.03 

9.92 

9.81 

9.72 

9.67 

9.62 

9.60 

9-52 

4i 

10.27 

10.  18 

10.13 

10.  IO 

10.09 

IO.II 

10.08 

10.04 

42 

10.54 

10.51 

10.52 

10.54 

10.60 

10.64 

10.64 

1  0.60 

43 

10.89- 

10.93 

10.98 

11.08 

n.  16 

11.22 

11.23 

11.22 

44 

11.32 

11.40 

10.54 

11.66 

11.77 

11.85 

11.89 

Il.Sg 

45 

n.  Si 

11.99 

12.15 

12.30 

12.43 

12.54 

12.  6l 

12.64 

46 

12.42 

12.62 

12.  8l 

12.99 

I3-I5 

13.29 

13-39 

13-45 

47 

13-07 

i3-3i 

13-53 

13-74 

13-94 

14.11 

14.24 

H-3I 

48 

13-79 

14.05 

14-32 

H-57 

14.80 

15.01 

15-15 

•15-36 

49 

14.56 

14.87 

15-17 

15-47 

15-74 

15-97 

16.16 

l6.30 

50 

15-41 

15-76 

16.11 

16.45 

16.74 

17.02 

17.24 

17-39 

5i 

16.34 

> 

16.74 

17-13 

17.49 

I7-85 

18.16 

18.40 

18.59 

52 

17-35 

17.80 

18.22 

18.65 

19.04 

19,38 

19.67 

19.90 

53 

18.45 

18.93 

19.42 

19.90 

20.31 

20.70 

21.04 

21.36 

54 

19.63 

20.18 

20.72 

21.22 

21.70 

22.15 

22.59 

22.96 

55 

20.93 

21-53 

22.10 

22.67 

23.21 

23-77 

24.27 

24.71 

56 

57 

22.33 
23-83 

22.97 
24-54 

23.61 
25.26 

24.25 
26.01 

24.90 
26.75 

25-53 
27.46 

26.12 
28.11 

26.6l 
28.70 

58 

25.46 

26.26 

27.10 

27.94 

28.77 

29.56 

30-31 

30-97 

59 

27-25 

28.18 

29.11 

30-05 

30-97 

31.86 

32.69 

33-43 

60 

29-25 

30.27 

3I-32 

32-34 

33-37 

34-36 

35-28 

36-13 

134  PRINCIPLES  AND  PRACTICE 

TABLE   No.    LV. 

COST  OF  INSURANCE  PER  $1,000  OF  A  TWENTY-FIVE  YEAR  ENDOWME-XT 
POLICY,  DURING  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7-13 

7.04 

6.94 

6.85 

6.74 

6.61 

6.49 

6-34 

21 

7.21 

7-13 

7.04 

6.94 

6-83 

6.71 

6-59 

6-45 

22 

7-3° 

7-22 

7-13 

7-03 

6-93 

6.81 

6.69 

6-55 

23 

7.40 

7-32 

7-23 

7.14 

7.04 

6-93 

6.8i 

6.68 

24 

7-50 

7.42 

7-34 

7-25 

7-i5 

7.04 

6-93 

6.80 

25 

7.60 

7-53 

7-45 

7-37 

7.27 

7.17 

7.06 

6.94 

26 

7.71 

7.64 

7-57 

7-49 

7.40 

7-30 

7.19 

7.07 

27 

7-83 

7-77 

7.70 

7.62 

7-54 

7-44 

7-34 

7.21 

28 

7.96 

7-9° 

7.84 

7.76 

7.68 

7-59 

7.48 

7-36 

29 

8.08 

8.04 

7.98 

7.91 

7.84 

7-74 

7.64 

7-52 

30 

8.24 

8.19 

8.14 

8.07 

7-99 

7.90 

7.80 

7.67 

31 

8.39 

8-35 

8.30 

8.23 

8.16 

8.07 

7.96 

7-85 

32 

8.55 

8.51 

8.46 

8.40 

8-33 

8.24 

8.14 

8.02 

33 

8.72 

8.68 

8-63 

8-58 

8.50 

8.42 

8.32 

8.20 

34 

8.89 

8.86 

8.82 

8.76 

8.69 

8.61 

8.50 

8.38 

35 

9.08 

9-°5 

9.00 

8-95 

8.88 

8.80 

8.69 

8-59 

36 

9.27 

9-24 

9.20 

9->S 

9.08 

9.00 

8.92 

8.87 

37 

9-47 

9-44 

9.40 

9-35 

9.29 

9-23 

9.20 

9.21 

33 

9.68 

9-65 

9.61 

9-57 

9-53 

9-52 

9-56 

9.60 

39 

9.90 

9.87 

9.84 

9.82 

9-83 

9.89 

9.96 

10.08 

40 

10.12 

IO.IO 

10-09 

10.13 

IO.2I 

10.31 

10.47 

10.60 

4i 

10.36 

10.37 

10.42 

10.52 

10.64 

10.83 

10.99 

11.17 

42 

10.63 

10.70 

10.82 

10.97 

II.I8 

11.38 

11.48 

11.78 

43 

10.98 

II.  12 

11.29 

11.52 

11.76 

12.  OO 

12,22 

13.45 

44 

11.41 

1  1.  60 

11.86 

12.12 

12-39 

12.66 

12-93 

13.18 

45 

Il.gi 

12.19 

12.48 

12-77 

13.07 

13-38 

13.68 

13.09 

46 

12.51 

12.83 

i3-'5 

I3-48 

13-82 

14.17 

H-51 

14.86 

47 

I3-I7 

13-53 

13.88 

14.25 

14.63 

15.02 

15.42 

I5-78 

48 

I3.S9 

14.28 

14.68 

I5.IO 

I5-52 

15.96 

16.37 

16.80 

49 

14.67 

15.10 

i5:55 

16.01 

16.49 

16.95 

17-43 

17.90 

50 

I5-52 

16.00 

16.50 

17.01 

I7-52 

18.05 

18.57 

19.06 

51 

16.45 

16.98 

i7-5i 

18.08 

18.65 

19.23 

19.77 

20-33 

52 

17.46 

18.05 

18.63 

19.25 

I9.S7 

20.47 

21.09 

21.  7O 

53 

18-57 

19.19 

19.84 

20.:;  i 

21.  l6 

21.84 

22.51 

23.24 

54 

19.74 

20.44 

21.15 

21.85 

.22.57 

23-31 

24.11 

24.90 

55 

21.05 

21.80 

22.54 

23-3I 

24.11 

24.97 

25-83 

26.73 

56 

22-45 

23.24 

24.06 

24.90 

2v82 

26.75 

27.72 

28.69 

57 

23-95 

24.81 

25.70 

26.68 

27-68 

28.72 

29.76 

30.83 

53 

25-59 

26.53 

27-55 

28.61 

29.72 

30.84 

3^99 

33-  *  5 

59 

27-37 

28.45 

29.56 

30-73 

31.92 

33-15 

34-40 

35-66 

60 

29-37        30-54 

3i-77 

33-02 

34-33 

35-66 

37-oi 

38-38 

OF  LIFE  INSURANCE. 


'35 


TABLE  No.  LVI. 

COST  OF  INSURANCE  PER  $1,000  OF  A  THIRTY- YF.AR  ENDOWMENT  POLICY, 
DURING  VARIOUS  YEARS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

First 
year. 

Second 
year. 

Third 
year. 

Fourth 
year. 

Fifth 
year. 

Sixth 
year. 

Seventh 
year. 

Eighth 
year. 

2O 

7.17 

7-13 

7.08 

7-03 

6.98 

6.92 

6.85 

6.80 

_  i 

7.26 

7.21 

7.17 

7-13 

7-07 

7-O2 

6-95 

6.89 

22 

7-34 

7-31 

7.27 

7-22 

7.18 

7-13 

7.07 

7-01 

23 

7-44 

7.41 

7-37 

7-33 

7.29 

7.24 

7.19 

7-13 

24 

7-54 

7-51 

7-47 

7-44 

7.41 

7-36 

7-3i 

7.26 

25 

7.64 

7.62 

7-59 

7-56 

7-53 

7-49 

7-45 

7.40 

26 

7.76 

7-73 

7-72 

7.69 

7.66 

7-63 

7-59 

7-54 

27 

7.87 

7.86 

7.84 

7-83 

7.80 

7-78 

7-73 

7.69 

28 

S.oo 

7-99 

7.98 

7-97 

7-95 

7-93 

7-89 

7-85 

29 

8.14 

8.14 

8.,  3 

8.12 

S.ii 

8.08 

8.05 

8.01 

30 

8.28 

8.28 

8.29 

8.28 

S.2r) 

8.25 

8.22 

8.18 

31 

8-43 

8.44 

8-45 

8-44 

8-43 

8.42 

8.3S 

8-35 

32 

8.60 

8.61 

8.61 

8.61 

8.61 

8-59 

8-57 

8-54 

33 

8.77 

8.78 

8.79 

8-79 

8.78 

8.78 

8.7  , 

8.71 

34 

8.94 

8.96 

8.97 

8-97 

8-97 

8.97 

8-94 

8.91 

35 

9.12 

9-15 

9.16 

9.17 

9.17 

9.16 

9^5 

9-J3 

36 

9-32 

9-34 

9-36 

9.37 

9-37 

9-37 

9-37 

9.42 

37 

9-5i 

9-54 

9-56 

957 

9-.SS 

9.60 

9.66 

9-77 

38 

9-73 

9-75 

9-77 

9-79 

9.82 

9-9° 

IO.O2 

10.  18 

39 

9-94 

9-97 

10.00 

10.04 

10.13 

10.27 

10.44 

10.67 

40 

10.17 

IO.2O 

10.25 

10.35 

10.51 

10.70 

10.95 

II.  21 

4i 

10.41 

10-47 

10.58 

10.75 

10.95 

11.23 

11.48 

II.80 

42 

10.68 

I  O.8O 

10.98 

1  1.  20 

11.49 

11.79 

12.  II 

12.43 

43 

1  1.  02 

11.22 

"•45 

11.76 

12.08 

12.42 

12.76 

13.12 

44 

11.46 

II.7O 

12.03 

I--36 

12.72 

13.08 

13-47 

I3-87 

45 

11.96 

12.30 

12.615 

13.01 

I3-4I 

13.82 

14.24 

14.69 

46 

12.57 

12.93 

J3-33 

13-73 

14.16 

14.61 

15.09 

I5-58 

47 

13.22 

12.63 

14.06 

i4-5i 

14.98 

15.48 

16.00 

16.52 

48 

J3-94 

H-39 

14.86 

15-35 

15.88 

16.42 

16.97 

17-55 

49 

14.72 

15.21 

15-73 

16.27 

16.85 

17.42 

18.04 

18.66 

50 

15-57 

16.  ii 

16.68 

17.27 

17.87 

18.52 

19.18 

I9.83 

51 

16.50 

17.09 

17.71 

18.34 

19.01 

19.70 

20.39 

21.  II 

52 

i7-5i 

18.16 

18.81 

19-Si 

20.23 

20.95 

21.70 

22.49 

53 

18.02 

19.29 

20.02 

20.77 

21.52 

22.^1 

23-  '3 

24.02 

54 

19.79 

20.54 

21.32 

22.  IO 

22.92 

23.78 

24.72 

25.68 

55 

21.09 

21.90 

22.70 

23-56 

24-45 

25.42 

26.43 

27.50 

136 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LVII. 

NET  SINGLE  PREMIUMS  PER  $1,000  FOR  A  TEMPORARY  INSURANCE  FROM 

ONE  TO  FIFTEEN  YEARS  (MASSACHUSETTS  NoN-FoRFEITURE  LAW,) 

COMBINED  EXPERIENCE,  4  PER  CENT. 


Ages. 

20 

22 

22 

23 

24 

25 

2G 

27 

Tears. 

I 

7-01 

7.09 

7.17 

7.27 

7-37 

7-47 

7-58 

7.70 

2 

I3-73 

13-94 

14.12 

H-3I 

H-50 

14.71 

M-93 

15.16 

3 

20.32 

20.57 

20.83 

21.  II 

21.40 

21.72 

22.05 

22.40 

4 

26.64 

26.98 

27.32 

27.70 

28.09 

28.51 

28.95 

29-43 

5 

32.76 

33-17 

33-61 

34.08 

34-57 

58.10 

35-66 

36-25 

6 

38.67 

39-  i  7 

39-70 

40.26 

40.86 

41.49 

42.17 

42.88 

7 

44.40 

44.98 

45.60 

46.26 

46.96 

47.70 

48.49 

49-33 

8 

49-95 

50.62 

5'.33 

52.08 

52.88 

53-74 

54-64 

55-59 

9 

55-33 

56.08 

56.88 

57-74 

58.64 

59.60 

60.  6  1 

61.68 

10 

60.  ?4 

61.39 

62.28 

63-23 

64.24 

65-30 

66.43 

67.61 

n 

65.61 

66.54 

67.52 

68-57 

69.68 

70.85 

72.08 

73-38 

12 

70.52 

7i-54 

72.62 

73-76 

74-97 

76.25 

77-58 

78.99 

13 

75-30 

76.41 

77-57 

78.81 

80.12 

81.49 

82.94 

84.46 

H 

7994 

81.14 

82.29 

83-73 

85-I3 

86.60 

88.16 

89.79 

15 

84.46 

85-74 

87.08 

86.50 

90.00 

91.58 

93-23 

94.98 

Ages. 

28 

29 

so 

31 

32 

33 

34 

35 

Years. 

I 

7-83 

7.96 

8.10 

8.25 

8.41 

8.58 

8-75 

8-93 

2 

I5-4I 

15.68 

15-97 

16.27 

16.58 

16.91 

17.26 

17.62 

3 

22.78 

23.18 

23.61 

24.06 

24-53 

25.02 

25-53 

26.06 

4 

29-93 

3°-47 

31.04 

3I-63 

32.26 

32.91 

35-59 

34-30 

5 

36.89 

37-55 

38.26 

39.00 

39-78 

40.58 

4i-43 

42-31 

6 

43-64 

44-44 

45-28 

46.17 

47.09 

48.05 

49.06 

50.11 

7 

50.21 

5i-H 

52.12 

53-H 

54-21 

55-33 

56-49 

57-7i 

8 

^6.60 

57.66 

58.76 

59-93 

61.14 

62.41 

63-73 

65.14 

9 

62.81 

63-99 

05.24 

66.54 

67.89 

69.31 

70.81 

72-43 

10 

68.86 

7o-i7 

7i-54 

-    72.97 

74-47 

76.05 

77-75 

79-63 

ii 

74-74 

76.18 

77.67 

79.24 

80.90 

82.67 

84.62 

86.78 

12 

8048 

82.03 

83-65 

85-37 

87.21 

89.22 

9*-43 

93-92 

13 

86.06 

87-73 

89.49 

91-38 

93-44 

95-7i 

98.24 

101.06 

H 

91.49 

93-30 

95-23 

97-33 

99-63 

102.19 

105.03 

108.20 

15 

96.79 

98.76 

100.90 

103.23 

105.81 

108.67 

111.84 

"S-34 

4r«- 

3d 

37 

38 

39 

40 

41 

42 

43 

Years. 

I 

9.12 

9-31 

9-53 

9-74 

9.96 

10.24 

10.48 

10.82 

2 

17.99 

18.38 

18.80 

19.22 

19.67 

20.17 

20.77 

21.51 

3 

2!'.63 

27.22 

27-83 

28.47 

29.l6 

29.96 

30.94 

32.12 

4 

35-04 

35-82 

36-63 

37-49 

38.47 

39-63 

41.03 

42.69 

5 

43-23 

44-20 

45-22 

46.36 

47.68 

4>23 

51.10 

53-27 

6 

51.21 

52-38 

53-66 

55-12 

56.81 

58.82 

61.17 

63-87 

7 

59.00 

60.42 

61.99 

63-81 

65-93  . 

68.39 

71.24 

74-47 

8 

66.66 

68.36 

70.27 

72.50 

75-05 

77.98 

81-33 

85.10 

9 

74.22 

76.25 

78..  S3 

81.17 

84-17 

87-57 

91.44 

95-72 

10 

Si-73 

84.12 

86.79 

89-85 

93-30 

97.19 

101.58 

106.43 

ii 

89.22 

91.98 

95-05 

98-54 

102.45 

106.84 

111.76, 

117.18 

12 

96.71 

99-85 

103.33 

107.25 

111.63 

116.52 

121.99 

127.97 

13 

104.21 

107.74 

111.63 

"5-99 

120.84 

126,25 

132-25 

138.81 

14 

111.71 

"5-63 

"9-95 

124.76 

I3O.IO 

136.01 

142.56 

149.70 

15 

119.23 

123-55 

128.30 

133-57 

139-39 

145.82 

152.91 

160.61 

OF  LIFE 


137 


TABLE  No.  LVII— (CONTINUED.) 

NET  SINGLE  PREMIUMS,  PER  $1,000,  FOR  A  TEMPORARY  INSURANCE  FROM 

ONE  TO  FIFTEEN  YEARS  (MASSACHUSETTS  NoN- FORFEITURE  LAW) 

COMBINED  EXPERIENCE,  4  PER  CENT. 


Ages. 

44 

45 

46 

47 

48 

49 

50 

51 

Tears. 

I 

11.25 

11.74 

12-35 

13.00 

I3-7I 

14.48 

15-33 

16.25 

2 

22.41 

23-47 

24.68 

26.00 

27.44 

29.00 

30.70 

32.56 

3 

33-55 

35-18 

37-03 

39-02 

41.19 

43-56 

46.14 

48.95 

4 

44.68 

46.91 

49-38 

52.07 

55-00 

58.17 

61  64 

65-39 

4 

55-83 

58.65 

61.77 

65.16 

68.85 

72.86 

77-2i 

81.91 

6 

66.98 

70.41 

74.20 

78.3' 

82.77 

87-59 

92-83 

98.50 

7 

78.16 

82.21 

86.67 

96.74 

102.40 

108.53 

115.13 

8 

8937 

94.06 

99.20 

104.76 

110.77 

117.26 

124.27 

131.80 

9 

100.63 

105.94 

111.78 

118.07 

124.86 

132.17 

140.04 

148.51 

10 

111.94 

117.88 

124.41 

131.43 

138.98 

147.11 

I55-85 

165.28 

ii 

123.29 

129.88 

137.10 

144.83 

I53-I5 

162.08 

171.72 

182.09 

12 

HI-93 

149.82 

158.26 

167-34 

177.11 

187.62 

198.93 

13 

146.15 

154.01 

162.57 

I7I-73 

181.58 

192.17 

203.56 

215.76 

14 

157-63 

166.  12 

175-34 

185.24 

195.86 

207.26 

219.48 

232-55 

15 

169.13 

178.25 

188.17 

198.78 

210.16  |  222.34 

235-37 

249.28 

Ages. 

53 

53 

54 

55 

56 

57 

58 

59 

Tears. 

I 

17.26 

18.36 

19-53 

20.83 

22.24 

23-73 

25-37 

27.16 

2 

34.60 

36.78 

39.16 

41-75 

44-53 

47-52 

50.80 

54-42 

3 

51-99 

55-29 

58.86 

62.72 

66.88 

71-37 

76.31 

81-73 

4 

69.47 

73-87 

78.61 

83-74 

89.27 

95-30 

101.89 

109.10 

5 

87.02 

92.50 

98.42 

104,81 

111.75 

119.28 

127.51 

136.45 

6 

104.61 

111.18 

118.26 

12595 

134.28 

I43-3I 

163.76 

7 

122.25 

129.90 

138.18 

U7-I.5 

156-85 

167.32 

178^68 

190.95 

8 

139-93 

148.69 

158.14 

168.38 

179.40 

191.29 

204.13 

217.94 

9 

I57-67 

167.52 

178.14 

189.60 

210.92 

215.17 

229.40 

244.67 

10 

175-45 

186.38 

198.13 

210.78 

224.34 

238.87 

254.42 

271.01 

ii 

193.26 

205.23 

218.09 

231.87 

246.61 

26^.33 

279.08 

296.85 

12 

211.06 

224.05 

237.96 

252.81 

268.64 

285.46 

303-27 

322.08 

13 

228.83 

242.79 

257.68 

273-55 

290-37 

308.14 

326.89 

346.59 

H 

246.53 

261.40 

277.21 

293.98 

311.67 

330-29 

349-84 

370.27 

15 

264.10 

279.82 

296.46 

314.02 

332-48 

372.01 

393-01 

4f«- 

6O 

61 

62 

63 

64 

65 

66 

67 

i 

29.17 

3I-36 

33-77 

36.38 

39-25 

42-39 

45-78 

49-49 

2 

58.41 

62-77 

67-53 

72.70 

78-35 

84.47 

91.10 

98.28 

3 

87.69 

94.17 

101.22 

108.87 

117.16 

126.13 

I35-78 

146.13 

4 

116.97 

I25-51 

134-77 

144-77 

I55-58 

167.19 

179.60 

192.86 

5 

146.19 

156.72 

168.09 

180.32 

'93-45 

207.47 

222.40 

238.26 

6 

I75-29 

187.71 

2OI.O7 

2I5-36 

230.60 

246.80 

263.97 

282.12 

7 

204.18 

218.39 

233-57 

249.72 

266.88 

285.01 

304-I3 

324.21 

8 

232.79 

248.63 

283.26 

302.12 

321-93 

342.68 

9 

260.98 

278.28 

296.59 

3I5-89 

336.16 

357-36 

379-45 

402.38 

10 

288.63 

307-24 

326.84 

347-31 

368.84 

391.16 

414.26 

438.08 

ii 

3I5-63. 

335-38 

356.07 

377-55 

400.01 

423.16 

446.95 

471.33 

12 

34I-87 

362.56 

384.12 

406.39 

429.52 

453-20 

477.40 

502.03 

13 

367.  21 

388.66 

410.87 

433-69 

457-23 

481.19 

505-5I 

530.06 

H 

391-54 

41.3-54 

436.20 

459-32 

483.05 

507-03 

53I-I9 

555-38 

15  !  4H-74 

459.98 

483.21 

506.88 

530-63 

554-37 

577-95 

PRINCIPLES  AND  PRACTICE 


TABLE   No.  LVIII. 

SHOWING  INSURANCE  DUE  ON  WHOLE  LIFE  POLICIES,  ACCORDING  TO 
THE  MASSACHUSETTS  NON- FORFEITURE  LAW. 


No.  of 
Prttn  iu  tns 

Age  2O. 

Age  21. 

Age  22. 

Age  23. 

Age  24. 

paid. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

I 

-    256 

263 

..    271 

..    278 

..    285 

2 

I    I5S 

I    169 

I    184 

I    I99 

I    213 

3 

2     6l 

2     83 

2    IO5 

2    127 

2     H9 

4 

2    341 

3    4 

3    33 

3    62 

3    9° 

5 

3   264 

3   299 

3   334 

4    3 

4    38 

6 

4   194 

4   235 

4   275 

4   3i6 

4   355 

7 

5   128 

5   175 

5    222 

5   268 

'  5   3H 

8 

6    68 

6    121 

6   172 

6   224 

6   276 

9 

7    ii 

7    69 

7   127 

7   185 

7   243 

10 

7   324 

8     22 

8    85 

8   149 

8    211 

ii 

8   276 

8   344 

9    47 

9   "3 

9   175 

12 

9   231 

9   303 

10    6 

10    68 

10    120 

13 

10   iS^; 

10   254 

10   3i5 

10   364 

ii    37 

H 

ii   128 

ii   186 

ii   233 

ii   267 

ii   291 

15 

12    47 

12    91 

1.2    121 

12   142 

12    149 

No.  of 

Age  25. 

Age  26. 

Age  27. 

Age  28. 

Age  29. 

Prem  111  ins 
paid. 

Years.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

I 

293 

300 

••    307 

315 

322 

2 

I    228 

I    242 

I    257 

I    271 

I    286 

3 

2    170 

2    192 

2    213 

2    234 

2    255 

4 

3   "9 

3   146 

3   174 

3    202 

3   230 

5 

4    72 

4   107 

4   HI 

4   176 

4   211 

6 

5    3i 

5    72 

5   "3 

5   i54 

5   196 

7 

5   36o 

6    42 

6    89 

6   137 

6   184 

8 

6   328 

7    iS 

7    69 

7   121 

7   168 

9 

7   3oo 

7   357 

8    46 

8    94 

8   134 

10 

8   272 

8   326 

9    7 

9    44 

9    7i 

n 

9   229 

9   273 

9   307 

9   329 

9   34i 

12 

10   161 

10   191 

IO    2IO 

10   218 

10   216 

13 

ii    64 

ii    79 

II     84 

ii    77 

ii    60 

H 

ii   302 

ii   302 

II    292 

ii   270 

ii   242 

i5 

12    145 

12   130 

12    105 

12      72 

12     26 

No.  of 

Age  3O. 

Age  31. 

Age  32. 

Age  33. 

Age  34. 

paid. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

Tears.  Days. 

I 

329 

337 

344 

••    352 

..    362 

2 

I    300 

i   3i5 

i   330 

i   345 

I    360 

3 

2    277 

2    299 

2    321 

2   343 

3      2 

4 

3   259 

3   288 

3   3i7 

3   347 

4    14 

5 

4   246 

4   282 

4   3i8 

4   356 

5    26 

6 

5   238 

5   279 

5   320 

5   356 

6    20 

7 

6   229 

6   272 

6   307 

6   334 

6   35i 

8 

7   210 

7   243 

7   266 

7   280 

7   284 

9 

8   164 

8   183 

8   193 

8   193 

8   186 

10 

9    87 

9    92 

9    88 

9    78 

9    53 

ir 

9   343 

9   335 

9   319 

9   291 

9   257 

12 

10   203 

10   183 

10   150 

IO    112 

10    72 

13 

ii    36 

10   363 

10   321 

10   270 

10   214 

H 

II    200 

"   153 

ii    98 

II     38 

10   338 

15 

II  341 

ii   282 

ii   218 

II    148 

ii    74 

OF  LIFE  INSURANCE. 


TABLE   No.  LVIII.— (CONTINUED.) 

SHOWING  INSURANCE  DUE  ON  WHOLE  LIFE  POLICIES,  ACCORDING  TO 
THE  MASSACHUSETTS  NON-FORFEITURE  LAW. 


No.  of 

Age  35. 

Age  36. 

^Ifire  37. 

Age  38. 

^Ifire  39. 

paid. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

1 

i           3 

I           II 

I            20 

I           29 

i         39 

2 

2            12 

2           29 

2         47 

2            65 

2            82 

3 

3        27 

3           52 

3        69 

3         99 

3       "5 

4 

4        46 

4        74 

4        98 

4       114 

4       123 

5 

5         56 

5         78 

5        93 

5         99 

5         96 

6 

6        41 

6         52 

6        56 

6        49 

6        36 

7 

6       359 

6       359 

6       349 

6       332 

6       307 

8 

7       280 

7       266 

7       245 

7       216 

7       181 

9 

8       167 

8       142 

8       109 

8        69 

8         24 

10 

9         24 

8       35i 

8      308 

8       258 

8          202 

ii 

9       215 

9       167 

9       "3 

9         59 

8       354 

12 

10         14 

9       32i 

9       258 

9       193 

9       116 

13 

10       152 

10        85 

10         13 

9       3°i 

9       219 

H 

10       267 

10       191 

10       114 

10         24 

9       299 

15 

10       359 

10       274 

10       184 

10         91 

9       359 

No.  of 

Age  4O. 

Age  41. 

Age  42. 

Age  43. 

^lf/e  44. 

Pretn  ititns 
paid. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

I 

I           49 

i         57 

I           64 

i         66 

I           65 

2 

2            96 

2       106 

2          IO9 

2        106 

2            98 

3 

3       "5 

3       128 

3       123 

3       "i 

3        95 

4 

4       123 

4       116 

4       102 

4        81 

4        56 

5 

5         86 

5         69 

5         45 

5         i5 

4       344 

6 

6         16 

5       353 

5       3i8 

5       279 

5       234 

7 

6       276 

6       238 

6       194 

6       144 

6        88 

8 

7       139 

7         9i 

7        38 

6       344 

6       282 

9 

7       337 

7      280 

7       217 

7       I51 

7         81 

10 

8       141 

8         76 

8          5 

7       295 

7       217 

ii 

8      285 

8          210 

8       132 

8         49 

7      327 

12 

9        38 

8       320 

8       234 

8       H3 

8        50 

13 

9       J33 

9        42 

8      3^3 

8       216 

8       117 

H 

9       205 

9       108 

9          7 

8       269 

8       164 

15 

9       258 

9       J54 

9        48 

8       304 

8       194 

JV0.  o/ 

-f  !7<-  45. 

Age  46. 

^.fire  47. 

Age  48. 

Age  49. 

paid. 

Tears.    Days. 

Tears.    Days. 

Tears.    Days. 

Tears.     Days. 

Tears.    Days. 

I 

i         61 

i        55 

I           48 

I           40 

I           32 

2 

2         86 

2            72 

2        57 

2           41 

2             24 

3 

3        75 

3        52 

3        28 

3         16 

2         340 

4 

4        26 

3       359 

3       325 

3       289 

3       253 

5 

4      306 

4       262 

4       220 

4       176 

4       131 

6 

5       184 

5       135 

5        80 

5        3° 

4      342 

7 

6        34 

6        14 

5       280 

5       218 

5       156 

8 

6      217 

6       150 

6        82 

6            12 

5      306 

9 

7        75 

6       333 

6          221 

6       143 

6        65 

10 

7       136 

7         53 

6       334 

6       249 

6       164 

ii 

7       239 

7       H9 

7         59 

6       332 

6       241 

12 

7      320 

7       224 

7       127 

7        3o 

6       299 

13 

8        15 

7       279 

7       T-77 

7        75 

6       339 

H 

8        58 

7      3i6 

7       210 

7       *°4 

6       364 

IS 

8        83 

7      338 

7      228 

7       120 

7         n 

140 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LIX 
DECIMAL  PART  OF  A  YEAR  FROM  ANY  DATE  TO  JANUARY  i,  FOLLOWING. 


Day. 

^aw. 

Feb. 

March. 

April. 

May. 

June. 

I 

.0000 

•9*51 

.8384 

•7534 

.6712 

•5863 

2 

•9973 

.9123 

•8356 

•7507 

•66S5 

•5836 

3 

•9945 

.9096 

.8329 

•7479 

.6658 

.5808 

4 

.9918 

.9068 

.8301 

•7452 

.6630 

•578l 

5 

.9890 

.9041 

.8274 

•7425 

.6603 

•5753 

6 

.9863 

.9014 

.8247 

•7397 

•6575 

.5726 

7 

.9836 

.8986 

.8219 

.7370 

.6548 

•5699 

8 

.9808 

•8959 

.8192 

•7342 

.65,1 

•5671 

9 

.9781 

.8932 

.8164 

•7315 

•6493 

•5644 

10 

•9753 

.8905 

•Si37 

.7288 

.6466 

.5616 

ii 

.9726 

.8877 

.8110 

.7260 

•6438 

•5589 

12 

.9699 

.8849 

.8082 

•7233 

.6411 

•5562 

13 

.9671 

.8822 

•8055 

•7205 

•6384 

•5534 

H 

.9644 

•8795 

.8027 

.7178 

•6356 

•5507 

15 

.9616 

.8767 

.8000 

•7i5i 

.6329 

•5479 

16 

•9589 

.8740 

•7973 

•7123 

.6301 

•5452 

17 

.9562 

.8712 

•7945 

.7096 

.6274 

•5425 

18 

•9534 

.8685 

.7918 

.7068 

.6247 

•5397 

19 

•9507 

.Sf-58 

.7890 

.7041 

.6219 

•5370 

20 

•9479 

.8630 

.7863 

.7014 

.6192 

•5342 

21 

•9452 

.8603 

.7836 

.6986 

.6164 

•53i5 

22 

•9425 

•8575 

.7808 

•6959 

•6i37 

.5288 

23 

•9397 

.8548 

.7781 

.6932 

.6110 

.5260 

24 

•9370 

.8521 

•7753 

.6904 

.6082 

•5233 

25 

•9342 

•8493 

•7726 

.6877 

•6055 

•5205 

26 

•93i5 

.8466 

.7699 

.6849 

.6027 

•5178 

27 

.9288 

.8438 

.7671 

.6822 

.6000 

•5i5i 

28 

.9260 

.8411 

.7644 

•6795 

•5973 

•5123 

29 

•9233 

.8411 

.7616 

.6767 

•5945 

.5096 

30 

.9205 

•75S9 

.6740 

.5918 

.5068 

31 

.9178 

.7562 

•5890 

ist  Mo. 

ad  Mo. 

jd  Mo. 

4th  Mo. 

Jth  Mo. 

6th  Mo. 

OF  LIFE  INSURANCE. 


141 


TABLE  No.  LIX  (CONTINUED.) 
DECIMAL  PART  OF  A  YEAR  FROM  ANY  DATE  TO  JANUARY  i,  FOLLOWING. 


July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Day. 

.5041 

.4192 

•3342 

.2521 

.1671 

.0849 

I 

.5014 

.4164 

•3315 

•2493 

.1644 

.0822 

2 

.4986 

•4137 

.3288 

.2466 

.1616 

•0795 

3 

•4959 

.4110 

.3260 

•2438 

.1589 

.0767 

4 

•4932 

.4082 

•3233 

.2411 

.1562 

.0740 

5 

.4904 

•4055 

•3205 

.2384 

•1534 

.0712 

6 

.4877 

.4027 

•3178 

•2356 

•1507 

.068? 

7 

.4849 

.4000 

•3151 

•2329 

.1479 

.0658 

8 

.4822 

•3973 

•3r23 

.2301 

.1452 

.0630 

9 

•4795 

•3945 

.3096 

.2274 

.1425 

.0603 

10 

.4767 

.3918 

.3068 

•2247 

•1397 

•0575 

ii 

.4740 

•3890 

•3041 

.2219 

•1370 

•0548 

12 

.4712 

•3863 

.3014 

.2192 

.1342 

.0521 

13 

.4685 

•3836 

.2986 

.2164 

•1315 

•0493 

H 

•4658 

.3808 

•2959 

•2137 

.1288 

.0466 

15 

.4630 

•378i 

.2932 

.2ITO 

.1260 

.0438 

16 

.4603 

•3753 

.2904 

.2082 

•1233 

.0411 

i7 

•4575 

.3726 

.2877 

•2055 

.1205 

.0384 

18 

•4543 

•3699 

.2849 

.2O27 

.1178 

•0356 

19 

.4521 

.3671 

.2822 

.2OOO 

.1151 

.0329 

20 

•4493 

•3644 

•2795 

•1973 

.1123 

.0301 

21 

.4466 

.3616 

.2767 

•1945 

.1096 

.0274 

22 

•4438 

•3589 

.2740 

.1918 

.1068 

.0247 

23 

.4411 

•3562 

.2712 

.1890 

.1041 

.0219 

24 

•4384 

•3534 

.2685 

.1863 

.1014 

.0192 

25 

•4356 

•3507 

.2658 

.1836 

.0986 

.0164 

26 

•4329 

•3479 

.2630 

.1808 

•0959 

•0137 

27 

.4301 

•3452 

.2603 

.1781 

.0932 

.OIIO 

28 

•4274 

•3425 

•2575 

•1753 

.0904 

.0082 

29 

.4247 

•3397 

•2547 

.1726 

.0877 

•0055 

30 

.4219 

•3370 

.1699 

.0027 

31 

7th  Mo. 

8th  Mo. 

9th  Mo. 

loth  Mo. 

nth  Mo. 

1  2th  Mo. 

LIFE  INSURANCE  FORMULAE.* 

In  the  American  Table  of  Mortality  we  have  at  the  age  10 
100,000  persons  living  at  the  beginning  of  the  year,  and  during 
that  year  749  die  before  the  survivors  reach  the  age  n.  In  the 
application  of  algebraic  notation  to  life  insurance,  we  designate 
the  living  at  any  age  in  the  table  of  mortality  by  /„,  or  by  / 
with  the  number  denoting  the  age,  as  /10,  /„,  etc.  If  we  make 
#=10,  the  number  living  at  the  age  n  is  denoted  by  4+»  and 
at  12  by  4+z>  and  hence  we  have  a  series  of  living  at  all  ages, 
/10  +  /n+/12  ....  /95=4+4+i+4+s  •  •••/«»  the  oldest  age  in  the 
mortality  table  expressed  by  lo.  The  same  formula  will  apply 
if  we  make  any  other  number  in  the  table  =#,  as  4>+4i+4i» 
etc.  =/a+4+i+4+2j  etc.  But  since  4  is  the  number  living  at  the 
beginning  of  the  year,  and  4+i  the  number  living  at  the  end, 
the  probability  of  a  person  aged  x  surviving  during  the  year  is 

2*~- ,  and  at  the  end  of  each  of  two  years  is  -y^-H — y^-,  and  con- 

^x  ^x  LX 

sequently  the  probability  of  his  surviving  each  year  till  he  reaches 
the  age  95  is  expressed  by  the  formula,  *+ '  +  -y^-  +  *,* "  •  •  •  •  -7* 

4c  '•x  lx  ''x 

If  each  person  in  the  number/  should  pay  $i  at  the  beginning  of 
each  year  during  life  into  a  common  fund,  the  total  amount  paid  • 
would  be  4+4+1+4+2  '  •  •  •  lu  dollars,  and  the  average  amount 
which  each  person  living  at  the  age  x  would  pay  would  be 

-f--\ — ^p-  +  -^p-....  j-.     But  payment!  to  be  made  in  the  future 

lx  lx  fx  lx 

have  a  present  value  depending  upon  the  rate  of  discount  assumed, 
as  well  as  the  probability  of  living ;  and,  if  we  discount  each  term 
in  the  series  after  the  first  by  4  1-2  per  cent,  or  multiply  each  term 

after  the  first  by  — — ,  (— —  )  ,  (— — )  ,  etc.,  and  make  — — =vy 
J  1.045'  Vi.045/  '  Vi.045/  '  1.045 

*  In  these  formulae  the  life  insurance  symbols  of  Dr.  William  Farr,  as 
published  in  Circular  No.  39  of  the  New  York  Insurance  Department, 
have  been  adopted. 


OF  LIFE  INSURANCE.  143 

.  /_     v.  /,+!      v^L+t     vs.  1..+3          w-j*.  lu       ,P 

we  have  the  series  ~+  —  f2±+  —  f^-+  —  r^  ----  —  7  —  •    If  we 

lx  tx  lx          .  lx  lx 

multiply  the  numerators  and  denominators  of  this  series  by  -v 
raised  to  the  #th  power,  which  does  not  alter  the  value  of  the 


f       ..  V".  lx  .    ,+  , 

fractions,  we   have   -~+  -  -=—  f  —  •+  .       ... 

v*.  lx         v*.  lx  v*.  4  v*.  lx 

vu.  lu      _  _      .  D,     D  +1       D.,+a 

-jrT'     Making  v*.lx=um,  we  have  the  series    ~+     *      +     '    • 

»  •  *x  *-*x          *^x  ^x 

;.D?=p.+D,H..+D.+i+D,H..>  etc>;   and?  substituting  N>  for  a]i 

the  terms  in  the  numerator  up  to  and  including  the  oldest  age  in 

N 
the  mortality  table,  we  have  the  last  fraction  =j^»  a  formula  which 

is  applied  to  a  life  annuity,  the  first  payment  to  be  made  at  the 
beginning  of  the  year  at  age  *,  and  which  is  also  represented  by 
A* 

Since  Ax=  ^  +  —  Jl+1    H  —  j|"  *i  etcv  tne  temporary  annuity  of 

$i  for  one  year  is   =f  =      x~    x~1   =    Az,  =  I,    and     for     two 

years  is    g*.+  ^1  =   N^-N»+a   =  A^    and    for    n    years     is 

Na-Nz+n  _* 
Dz  A*»' 

The  present  value  of  an  annuity  deferred  for  three  years  is 
Na         Dg+Dg+i+Ds+a          D.+,  +  D,+4  +  D,+5.etc.,  _   NZJ±  and  in 

DX  '        -IDT  ~^T  ~    i>,  ' 

general,  the  expression  for  a  deferred  life  annuity  is    £+B  =A,|n. 

The  formula  for  a  deferred  temporary  annuity  to  commence 
after  n  years  and  to  continue  m  years,  is 


X 

The  number  of  deaths  at  any  given  age  x  is  expressed  by  d,. 
At  age  10  the  number  dying  during  the  year  is,  by  the  American 
Table  of  Mortality,  749,  and  hence  the  probability  that  a  person 

aged  10  years  will  die  during  the  year  is  ~^'^=  ~~f-  The 
probability  of  dying  during  each  of  the  first'  two  years  is 
yH — ^-,  and  we  have  the  following  series  representing  the 

'x  x 

J  J  J 

probability  of  a  life  aged  x  dying  each  year :  y5  -I-  •  •'+1  +  ^  + 
^•p*,  etc.  Since  ~  is  the  probability  of  dying  during  the  first 


144  PRINCIPLES  AND   PRACTICE 

year,  it  is  the  undiscounted  sum  required  to  insure  the  life  x  for 
$i  one  year,  or  payable  at  the  end  of  the  year.     The  premium 

required  payable  at  the  beginning  of  the  year  is    -f-    multiplied 

,  '* 

by  the  present  worth  of  $i,  or  —  ^-^and  for  two  years  is  $i  mul- 

,          2  l* 

tiplied  by  -^—  -  +  -  '     x+1,  and,  generally,  the  single  premium  to 


T/.  i       .     v.  d         vz  <£_+i  ,+t 

insure  a  life  aged  x  is  —  y*  +  •  —  f  --  1  --  -r  —  >  e*c<» 


.  .  .  .  etc. 


"•x 

Multiplying  both  numerator  and  denominator  by  z'*,  we  have 

<4xtr»+2.  dx+1xv*+s.  dx+,,  etc.       -D   ...  ,,1     ,         ~ 

-  ^-£  -  z  -  .     Putting   #»+*.  «?„  =  C.,   we 

,  ,,          •      i  •  C,.+  C,.+  i  +  Cx+a>  etc.  ,          .  . 

have   the    single  premium  =  —  -  -  ^—  —  -  :  -  ,  and,  making 

the  numerator  or  the  sum  of  all  the  C's  =  M,,  we  have  the 

M 
single  premium  =  ~,  which  we  represent  by  !!„. 

If  rrx  represents  the  annual  premium  on  a  life  aged  AT,  it  is 
evident  11,.,  the  single  premium,  is  the  present  value  of  the 
annuity  ffx,  or  the  annual  premiums  during  life.  Hence,  irx.  Ax=  Uj., 

n,       0.  M,         ,    .         Nz     Hx       Mx     Nx      MX 

and7r*=  A?    Since  ns  =  ^-,  and  Az=^,    _  =  --,^  =  -, 

the  net  annual  premium. 

The  annual  premium  on  a  limited  payment  life  policy  is  found 
by  dividing  the  single  life  premium  by  the  temporary  annuity  for 
the  number  of  years  in  which  the  payments  are  made: 

Ji,         M,  _  Nx-Nx+n  _          Mg 
*"•  -  A.  S'    D.  *          Dx  :   N^N^Tn- 

Term  Insurance.  —  We  have  seen  that  the  cost  of  insuring  a 


r  .      vl.  dx          Cx        Mx—  Mx+i        jf 

person  for  a  single  year  is  —  —  -  —  =  =r-  =  --  =—  ^  —  ,  and  for  two 

*V  •   t>x  •L'x  -^^a; 

years  is  ~  +  -~-  =  —  x    •  x+2,  and  therefore  the  single  pre- 

\Jx  *-*x  J-'aj 

mium  to  insure  a  life  for  n  years  is  —  *  _   X+TO.     To  find  the  annual 

premium,  we  divide  this  by  the  temporary  annuity  for  n  years, 
MX-MX+,,         Ng-Nz+n  _   Ma;-Ma.+n 
Dz  .   Dx  Nx-Nx+n' 

Endowment.  —  The  single  premium  required  to  purchase  the 
simple  endowment  of  $i  payable  n  years  hence,  if  the  insured 
lives,  is  the  discounted  number  of  the  living  at  the  age  x  +  n 


OF  LIFE  INSURANCE.  145 

V*+n.  I  + 

divided  by  the  discounted  number  of  living  at  age  x,  — ^T"/~ 
— ~— ,  and  the  annual  premium  is  found  by  dividing  the  single  pre- 
mium by  the  temporary  annuity  for  n  yer.rs,  — ^~  -. ~f>~^~Ji= 


Endowment  insurance. — This  is  a  combination  of  term  in- 
surance and  simple  endowment.  The  single  premium  on  an  en- 
dowment assurance  policy  payable  in  n  years  or  at  death,  if  prior, 
is  the  sum  of  the  single  premiums  of  a  term  and  a  simple  endow- 

r                          M,-MT+n        D,+n         MJ-MJ+K  +  Dx+n 
ment  policy  for  n  years  = ~-  -  +  — £)—  =  -        — -j^— 

and,  dividing  by  the  temporary  annuity  — x       J+n,  to  obtain  the 

i          ^1      c          i               M, — M_+n  +  P,+_ 
annual  premium,  we  have  the  formula  ^x  =  — f  . .  *  " — — . 

N*-NI+n 

For  an  endowment  insurance  payable  in  n  years  or  at  death,  if 
prior,  the  premiums  being  paid  annually  during  m  years,  ;;/  bejng 
less  than  n,  we  divide  the  single  premium  given  above  by  the 

temporary  annuity  of  $i  for  /;/  years,  irn  =  — ^ £^-i- 

Ng-NJ+Bt  _  M.-M,  +  n-DJ+n 
D,  Nz-N^m 

Annual  premium  during  n  years  to  insure  a  life  annuity  of  a 
dollars  at  age  x—n.  a.  Ax+n  =  present  value  of  the  annuity  a  at 
age  x  +  n.  This  is  the  quantity  to  be  insured  on  a  simple  endow- 

D,+_  IX+-  <*•  N,+_  a.  N,+_ 

ment,  or^-; — ~—  x   a.  Aa.+B  =  ^ — ^r—  x  *  "   =   ^ — •'— 

Nx-NI+n  Na-Nx+n  DJ+n  N,-NX+. 

Annual  premium  to  insure  b  dollars  to  the  age  x  +  n,  if  death 
occurs  within  n  years,  and  to  insure  a  life  annuity  of  a  dollars 
during  life  from  age  x+n.  Add  the  term  insurance  on  b  dollars 

, ,      ,     .  f          ,       a.  N.,+n  +  £(M,— M,+_) 

to  the  last  formula,  ^" — :..-* £±^. 

NI-Nx+n 

It  is  often  convenient,  especially  in  computing  joint-life  pre- 
miums, to  be  able  to  use  only  the  D  and  N  columns,  and  a 
few  formulas  are  given  explaining  the  method. 

Since  n,=  ^  +  *^±L  +  -*£±L,  etc.,  and  rf.-/.-/.+1> 
'*  '*  '« 

and    d.4 ,  =-  /.+1  _  /,+J,    etc.,    we    have    n,  _    t/(/'~/J+l)    + 

*• 

fV. -t.  .-/.*.)  +^O±1ZA±I/,  etc.     Separating  this  formula  into 
'•  l 


146  PRINCIPLES  AND  PRACTICE 

two  parts,  we  have 


_        r.r./r+it,  etc.)          v(Zx+i+v.lx+-i+v.Zx+s,  etc.) 
'  I,  /. 

x  -  A,+  ,  =  w.A,  -  (A,  _  ,)  =  i-Qi—  f)Ax,  and  TTX  = 


Single  premium^  life.  —  Making  z"  the  rate  per  cent, 

-.  A 


. 


Annual  premium  Jifc.—-t  =£  =  (1-7^7  x  ^-)  ^  = 
D,          /  i  / 


Whole  life  insurance  by  n  annual  premiums.  — 
,          x-(i-w)A,        r      y        N  N,  -|  Dz 

=     -  *-J  -  £  -     =  I  —  (i—  f)    TT—  X      —  XT      .   XT  --      = 

AiB  L  '  Dr  J  Nx—  Nx+n 


«-i+n  ,-a;+n  x-z+n  N  -N  + 

Endowment   insurance.  —  The   single   premium   for   a   tem- 
porary insurance  of  n  years  is 

rr   —  -   (lx+v-l*+t+yl>l*+*+v*Ix+s  •  •  •  •  'pn4+n) 
*  ~"  v.l, 


P.(N-~DN-+")  -  *(Nr+1  ""j^'*""")*  divided  by  the  temp°rary 

annuity,  ^T-^±i,v-  (Nj+'~^'"'M)  =    annual     premium 

— 


for  temporary  insurance.  Adding  the  single  premium  of  sim- 
ple endowment,  —  J^2-  to  the  single  premium  for  temporary 
insurance,  and,  since  Nx+n+,  +  DI+n  —  Na+n,  we  have  the  single 

premium  endowment  =  v  (  '  *~D-J^-5-  )  —  (    X+'D  —  ^^  )  and 

j»j  _  N  + 
dividing  by  the  term  annuity,  —  i~f)~j!L~i  we  have,  annual  pre- 

mium =  v  \-~^*_™  I+n  )    Net   annual   premium   for  n   years, 

payable  in  m  payments,   v  (—  ^r+l_N   '-"). 

Joint  lives.  —  We  have  seen  that  the  general  formula  for  an 
annuity  on  a  life  x  is  A,  =    ^.7,+.  +«»./.+.+*./,+.  >etc> 


OF  LIFE   INSURANCE.  147 

if  there  are  two  lives,  x  and  y,  the  result  of  a  combination  of  them 
will  be  their  product,  and 

A  lx-  l«  +  v-  '*+!•  ',,  +  i+f5-  /!+*•  la+i  +  vs  lx+3-  L  +  s,  etc.         ,         . 

A,  y  —   —  —  £-  —s  -  -  —  —  -H-  -  2  -  ,  and  mul- 

•«'  'y 

tiplying  by  T>%  we  have 

.  If    lx.     ly 


f 

,  etc.,  _ 


£>*., 

Ill  preparing  the  column  Dx.  y,  if  .*— 15  and  ^/— 10  years  ot 
age,  then  we  add  the  logarithm  of  Dxu  to  the  logarithm  of  yw 
or  /'°,  the  number  of  living  at  the  age  10,  which  gives  the 
logarithm  of  D,.  y,  and  the  log.  D16  +  log.  yn  =  log.  Dx+,.  y+1, 
and  so  on  throughout  the  column  D,.  The  numbers  corre- 
sponding to  these  logarithms  will  be  the  column  Dz.  y.  The 
column  N,  ,  is  found  b/  the  summation  of  the  column  D, 

J  *.  y 

With  the  D,..  y  and  N,.  ,,  columns  of  any  combination  of  ages, 
the  operations  in  joint  lives  are  performed  in  the  same  manner  as 
those  of  single  lives. 

Rcttirn  premium  plan. — This  plan  of  insurance  provides 
for  the  return  of  all  the  premiums  paid  when  policy  becomes  a 
claim.  In  this  kind  of  policy  there  are  two  parts  to  be  consid- 
ered, the  specified  sum  insured  and  the  part  constantly  increas- 
ing by  KX  each  year.  The  first  has  -  -  for  the  annual  pre- 
mium, and  the  latter  has  ^x  (~-  +  -\>— +  — vr~»  &c-'  )  =  "••T3? 
Putting  these  together,  we  have  -r^  +  KX.  -—•  =  *„•  Clearing  of 
fractions  M,  +  TTX  R,  =  w.  N2,  and  IT,  =  ,  M*  . 


Loaded  annual  premium. — Let  TT,  =  net  annual   premium 
and  ($1  + loading)  =  g.     Multiplying  -^  +    irx   ^/  =  ira  by  g^ 

•Nx  Na 

we  have  g  -^-  +  KS  g.  -^-  =  g.  TTX,  therefore, 

i\a  IN^ 

M. 

{?.     MX 

ff.    7TX    =     ~~    p-    =1 

A'     x 

rct  annual  premium  for  the  return  of  gross  premiums. — 
M. 


i 

itS  PRINCIPLES  AND  PRACTICE 

Limited-payment  annual  return  premium. — 
*m  **     NX-NX+W     +  *"  (    N.-N.+.     +     N.-N.+,    +     NZ-ZNX+B  ' 

r  +  n~"  * I     _^_  * J.      7T      |    _      x  ^  .      *__1^_     \ 

N»-Nx  +  n  '  N*-Nz  +  »  *   V      Nx-Nx  +  n     >/ 

Clearing  of  fractions,  Mx  -  «•„  (R,  -  Rx+n)  =  -x  (Nx  -  Ns+n), 


With  loading,  f.  ff. 


^  (Nx-Nz+n)    (Rx-Rx+n) 

T-,     ,  .  M,—  M,+.,4-D,+ 

Endowment,   ,„  -  -- 


IJT.,,      ,       ,. 

with  loadmg,  g.  ,. 


(N_N+J.(RjRn) 

M+    +  D+ 


j  (Nx-Nx+n)  -  (Rx-Rx+n) 

Single  return  premium. — Let  U,  =  single  return  premium, 

Ma  M. 

Uien  nx  -  -^  +  nx.  1^- 

nx.  D,  =XM,  +  nx.  IVT. 

Mx 

".  -    D^NiT_ 

Net  single  premium  for  the  return  of  grcss  premium. — 
Let  (i+/)  =£"=  $i  +  loading;  then 

n»  =  l£+^l>7n*'  whencc  n«  -  DX-M;M. 

Loaded  single  return  premium. — 

n  - 


VALUATION  OF  POLICIES. 

Let  TTX  be  the  annual  premium  payable  on  a  life  policy,  it  is 
evident  that  if  the  policy  were  not  subject  to  the  future  payment 
of  this  annual  premium,  the  value  of  it  would  be  the  single  pre- 
mium of  a  policy  of  assurance  on  a  life  aged  *  +  «  =  nx+n.  But 
in  consequence  of  the  charge  of  an  annual  premium  on  the 
policy,  the  value  will  be  reduced  by  a  sum  equal  to  the  value  of 
all  the  future  premiums,  or  the  present  value  of  an  annuity  of  nm 
on  a  life  equal  to  »+«,  the  first  payment  of  which  will  be  made 


OF  LIFE  INSURANCE.  149 

immediately,  and  the  formula  will  be  H.,.+n  =  n+n  —  irx  x  A^+^SB 
("-.+.  ~  **)  Ax+»-      But   ffx+»  =    T-1 (i-*0  and  TTX  .  i  _ 


Additional  formulae  for  the  value  of  whole  life  policies : 

TT  l~^x  +  n      TT  7Tx  +  n~7rx 

Value  of  a  life  policy  paid  up  by  m  premiums  is  at  the  end  ot 

N  +  — N  + 
n  years,  IIx+n  =  nx+B  —  TT,  — ~rT~ 

Value  of  an  endowment  policy  payable  in  m  years  or  at  pre- 
vious death, 

H    4-        =1    —    I  —^ £^2L     -3-    *   ^    *  +  n-[    =3:  i *+n— ro 

V  J-^z+n  *}*  '  A^ 

Also,  Hx+n  =  DI+n  -  TT, £±5Zl_i±»_ 

Here  nz+n  =  the  net  single  premium  of  a  policy  issued  at  the 
age  x  +  n  and  payable  at  the  age  x+m. 

Value  of  an  endowment  policy  payable  at  previous  death  or  in 
m  years  by  m  number  of  payments. 

Hx+n  =  nI+n  -  TTX.    NT+D~+^+OT>' 

Value  of  a  term  policy  to  expire  at  age  x+m. 


The  explanation  of  these  three  last  formula?  is  found  on 
page  46. 

Value  of  a  simple  endowment  policy.  In  this  form  of  policy 
the  company  does  not  assume  any  risk,  and  the  reserve  at  the 
end  of  any  given  year  is  the  reserve  of  the  previous  year  in- 
creased by  the  co-efficient  of  accumulation. 

HX+»  =  (Hx+m-i  +  *•*)   «x+»-«-      Also,  Uf+n  »=nsfB  -  TTB. 

j^-      }^ 

-£-  in  which  Ux+n  =  single  premium   at  age  x+n  to 

insure  policy  payable  at  x+m, 

-  D*+m  _3-±Jfi_  N,+M-N,+, 

"«+»  =  Di+n  NX-NZ+M  Dx+lt 


*5°  PRINCIPLES  AND  PRACTICE 

Wright's  Accumulation  Formula, — Let  Hi+1  =  the  value  of 
a  policy  at  the  end  of  the  first  year,  ct  =.  v  -—,  the  risk  of  $i  at 

*x 

the  age  #,  and  TTX  =  the  net  premium  paid,  then  we  shall  have 
I  :  cx : :  I— HI+, :  cx.  H,+1  ==  the  value  of  the  actual  risk  run  by 
the  company  on  $i  insured.  Subtracting  this  value  from  the  net 
premium,  and  accumulating  the  remainder  at  the  assumed  ratio 

of  interest  —  =  r,  we  have 
v 

HI+1  =  r  (•n-x—cie+cx.  Ha+j),  which  reduces  to 


Buti-r.c.=  (i- 


Representing  this  last  fraction  by  uz,  we  have  the  formula, 
H.,,+i  =  ux  (KX—C^  =  the  value  of  a  policy  at  the  end  of  the  first 
year.  The  value  at  the  end  of  the  second  year  is 

H^+2  =  ux+1  (HI+i  +  ?rx  —  0,+,),  and  generally 

HZ+B  =  «„+„_!  (H,+n_i  +  TTX  —  cI+n_,). 

Fackler's  Formula. — HI+n+1  =  (H4+0  +  ^  u,+n  —  /•„+„,  in 

which  kx+n  =  -=-x-±2-. 

Dx+n+l 

Me  ClintocK's  Formttla. — The  following  formula  gives  a  some- 
what shorter  process  than  the  two  preceding  ones. 

Let  us  suppose  a  group  of  /*+„-!  policyholders  assured  $1 
each,  and  having  a  reserve  for  each  one  of  !!,+„_,,  making  a 
total  present  reserve  for  the  group  amount  to  4+n_i  (!!,.+„_,). 

A  year  from  the  present  time,  after  adding  premiums  of  rix  each 
now  due,  and  increasing  the  sum  of  these  reserves  and  premiums 
by  interest  at  the  rate  of  i  +  r,  the  fund  will  have  amounted  to 
(i  +  r)  (H.,.+B  —  i  +irx)  /.,+„_!.  There  will  have  died  several  of 
the  group,  reducing  the  number  of  living  to  /„+„,  to  whose  heirs 
at  $i  each  the  sum  of  lx+n-\  —  4+»  dollars  are  paid.  The  fund 
is  then  reduced  to  i+  r  (H.jefH-l  +  -re,)  /*+„-!  +  (lx+n-\  —  4+«) 
=  4+1.-4+«-i  [i-(i+r)  (HI+n_,  +  «•«)].  Dividing  the  amount 
of  this  reserve  by  /x+n,  the  number  of  policyholders,  and  putting 

,+»-iC^  t»j.  _  ux+n-l  andg-=v— ?rx,  the  reserve  on  each  policy 

is  found  to  be  Hz+n  —  !-«,+„_, (^•-Hs+w_,). 

The  column  cx  or  kx  is  dispensed  with,  leaving  but  one  column 
ux  to  be  kept  on  hand  and  referred  to. 


OF  LIFE   INSURANCE.  15* 

Rule. — Subtract  the  net  premium  paid  on  each  $i  (and  last 
year's  reserve  on  each  $i  assured,  if  any)  from  the  present  value 
of  $i  due  one  year  hence.  Multiply  the  remainder  by  the  value 
of  u,  corresponding  to  the  party's  age  at  the  beginning  of  the 
year,  and  subtract  the  product  from  unity. 

ffomans's  Contribution  Formula. — Let  r  =  the  actual  rate 
of  interest  received,  e=  the  expenses,  and  •     *+n    (i— Hx+n+j) 
the  actual  cost  of  insurance,  then 

rf'x  +  n 

x+n  i'x  +  n  x  +  n  +  i 

contribution  to  surplus. 

Formulae  for  verifying  Commutation  Columns. — 
Cx  =  v.  Dx  —  Dx+i        MX  =  v.  Nx_!  —  NX  =  Dx  —  v.  Nx 
Rx  =  v.  Sx-,  -  Sx          Mx+n  =  v.  Nx+n-,  -  NI+n  = 
Rx+n  =  f.  Sx+n-t-SI  +  n. 

Equation  of  Life. — Let  lx=  the  number  of  living  at  age  #, 
—  the  number  of  living  at  the  age  of  equation,  4+B  the  number 

2 

of  living  at  the  beginning  of  the  year  in  which  the  equation  takes 
place,  /,+H+i  the  number  living  at  the  end  of  the  year,y=  the 
fraction  of  a  year,  which,  added  to  x+n,  will  make  the  equation 

then  —  =  /,+„+/  and  we  have 

2 

f  __  j=+n — x+n+/  substitutinjr  —  for  L±,^t 


7+  -^ 

**  +  n         2 
C  +  «.~  4  +  n+l 


Expectation  of  Life. — 


WRIGHT'S  FORMULA  FOR  INSURANCE  VALUES. 

Representing  the  insurance  value  at  the  age  x+n  by  X+B  L, 
we  have  the  general  formula, 

N  d"  N  **'•*• ' 

,  +  „!«  = ^-r-   X  — 

If  we  assume  x  =  10,  and  perform  all  the  multiplications  of 

j  «/i  i   . 

—  into  Nn,  and  -j —  into  N12,  &c.,  as  indicated  by  tlie  numera- 

/u  «n 


152  PRINCIPLES  AND  PRACTICE 

tor  three  lines  above,  the  summation  of  the  products,  after  the 
manner  in  which  the  N  column  is  produced  from  the  D,  will 
produce  a  column  of  numerators  which  we  will  call  A,  and  this 

will  give  us  x+n  1*=-^-  x  ^L,  and  x+nlx+t  =  -5^_   x 

x  +  n  **x  **m  «+*•"• 

x+"    x+t    when  the  policy  has  completed  /years  and  the  (/+  i)th 

premium  is  just  paid. 

The  formula  for  the  insurance  value  on  a  paid-up  policy  is 

r+ 


The  formula  for  any  policy  payable  at  age  x  +  n,  or  previous 
death,  including  the  ordinary  whole  life  policy,  is  thus  modified 
by  Mr.  McClintock.  Let  KX  be  the  annual  premium  to  be  paid 
q  times  and  when  the  first  premium  is  just  paid,  we  have 

j  T       x  +  n  'V»  *  +  y  A.X 

and  when  the  (/+i)th  premium  has  just  been  paid, 

T  !  ,7      *  +  nA*  +  <  .  +  ,**  +  , 

.+„  i.t,  |  i  -         D^-     T,    »x+t 

PROF.  BARTLETT'S  FORMULA  FOR  SURRENDER 

VALUES. 

Prof.  Bartlctt,  actuary  of  the  Mutual  Life  Insurance  Company 
of  New  York,  has  pi'oposed  the  following  formulae  for  finding 
the  surrender  value  of  a  policy,  which  is  based  upon  the  fol- 
lowing assumptions : 

A  reserve  of  an  individual  member  of  a  company  is  what  the 
company  should  have  to  the  member's  credit  at  a  given  epoch 
after  subducting  from  the  amonnt  paid  by  him,  augmented  by 
his  interest  earnings,  his  proportion  of  the  death  claims  that 
have  matured  up  to  the  same  epoch.  A  surrender  value  is  the 
amount  the  company  should  pay  to  abrogate  a  contract  between 
itself  and  one  of  its  members. 

By  the  terms  of  this  contract  the  company  promises  to  pay  to> 
the  heirs  of  the  assured  at  his  death,  whenever  that  may  hap- 
pen, a  certain  specified  sum  of  money.  And  the  assured  paysr 
in  consideration,  another  sum  down,  called,  let  us  suppose,  a 
single  net  premium,  which  is  the  present  net  value  of  the  assur- 
ance. This  premium  must  be  such  as  to  amount  at  compound 
interest  to  the  sum  assured,  should  the  assured  live  to  the  great- 


OF  LIFE  INSURANCE.  r$3 

est  age  of  the  tables,  and,  besides,  it  must  contribute  its  share  to 
the  payment  of  the  death  claims,  from  year  to  year,  of  other 
members  who  die  before  attaining  to  this  age  ;  and  this  obliga. 
tion  to  pay  death  claims  must  last  during  the  life  of  the  assured, 
which  life  is  assured  in  the  original  agi'eement  to  extend  to  the 
oldest  limit  of  the  tables  of  mortality  employed  in  computing  the 
premium. 

The  company  and  the  assured  have,  therefore,  joint  interest  in 
the  policy  of  the  latter.  The  present  money  values  of  these  in- 
terests being  found  at  the  time  of  the  surrender,  their  difference 
will  obviously  be  the  surrender  value. 

The  company's  interest  in  any  particular  policy  is  the  present 
value  of  the  sums  the  policy  would,  if  continued  in  the  company 
in  its  present  condition,  contribute  from  year  to  year  to  pay  death 
claims  on  other  policies. 

The  interest  of  the  assured,  or  of  his  heirs,  in  his  policy  is  the 
present  value  of  the  reversion  or  sum  the  latter  would  receive  at 
the  death  of  the  owner,  provided  he  pay  nothing  more  than  he 
has  already  paid.  This  interest  is  the  present  reserve. 

Make 

11^=  Single  net  premium  at  age  x  to  insure  one  dollar  at  death. 

R,  =  Net  reserve  on  policy  at  age  x  when  surrender  is  made. 

m  —  Number  of  years  the  policy  has  to  run  to  maturity. 

*z  =  Difference  between  the  oldest  age  of  tables  and  that  of 
policyholder  at  time  of  surrender. 

Vz  =  Present  value  of  one  dollar  due  in  x  years. 

tf=  Sum  assured  or  amount  of  policy. 

Life  Single  Premium. — Take  the  life  single  premium  as  a 
standard,  we  have  R,  =  TT,.  and  /;/  =  n. 

Denoting  the  surrender  value  by  Q_,  the  surrender  value  of  tf 
is  found  by  the  formula  : 
x-»  _          C.,.  Rj  +  i  +  Cr+\-  Rz+a  .  .  .  .    +   Cx  +  n  R^+,,  +  1 

Tabulate  the  numei'ator  of  the  second  member  under  the  head 
T,  after  the  manner  of  the  commutation  columns  N,  M,  S,  &c. 

Then    will    Q*.  =  a    -2f- (z) 

Life  Annual  Payments. — In  this  case 

T>  rr> 


154  PRINCIPLES  AND  PRACTICE 

Life,  Limited  Payments.  — 
R  T 

^-"-nT-lt   ......    (3) 

this  differing  from  the  last  case  only  in  the  value  of  R,. 

Temporary  Single  Premiums.  —  Here  the  formula  becomes  : 
Q  _          Cj.   RI+I  4-  Ci+i   RT+2    ....     Qr+pt—  i.   Rg  +  OT—  i 
^^ 


Cx.  Rx-H,  »*  — 

~~ 


Temporary  Anmial  Premium. 

o  --  a  -^r-  •   C*-R*+"  '"-1   /CN 

u  '.  ~~D~ 

ITa  being  the  single  premium  to  purchase  temporary  insurance 
of  $i  at  the  age  of  surrender. 

Simple  Endowments  —  Si):gle  Premium.  —  The  company  has 
no  interest  in  the  longevity  of  the  holder  of  this  kind  of  policy. 
On  the  contrary,  by  the  principle  of  the  Tontine,  its  interest  is  in 
his  early  death,  at  least  death  before  the  policy  matures. 

The  reserve  being  R,  there  are  lx  chances  for  and  against  the 
company.  Of  these  dx,  dx+l,  etc.,  to  t/1>+OT_1,  favor  lapse  by  death, 
and  the  surrender  value  is 

«*•*'••«*'+--') 

-  (6) 


Simple  Endowments  —  Annual  Premiums.  — 


Q_=..R,      *-a  (7) 

Endowment  Assurances  —  Single  Payment.  —  This  being  a 
combination  of  the  simple  endowment  and  temporary  insurance, 
the  surrender  value  is  found  by  taking  the  sum  of  equations  (4) 
and  (6). 

-  (S) 


Endowment  Assurances  —  Annual  Payment.  —  Here  take  the 
sum  of  equations  (5)  and  (7),  or 


.         .. 

The  reserves  Rz  and  R,  must  be  :   the  first  for  the  assurance 
part  of  the  policy,  the  second  for  the  endowment. 


OF  LIFE  INSURANCE. 


'55 


TABLE  No.  LX 

SURRENDER  VALUES.     LIFE  POLICY  FOR  $1.000,  ENTERED  AT  AGE  35, 
PAYABLE  AT  AGE  100,  OK  PREVIOUS  DEATH. 


BY  MR.  WHIGHT'S  METIIOH:  Sun  <ENDEK  CHAKGK,  8  PER 

PROF.   RANTLKTT'S 

CCNT  OF  INSUKANCK  VALUK. 

MbTIIOD. 

Combined   E.tpei  tence, 

Combined  Experience, 

American  Experience, 

4  pfr  cent. 
Actual  Prrm..  $26.38. 

6  per  cent. 
Actual  Prem.,  $20.45. 

*  fer  cent. 
Actual  Prem  .  $26.38. 

Age. 

Net  Prem  .  $1987 

Net  Prnn..  $16.49. 

Net.  Prem.,  $18.84. 

Surrender 

Surrender 

Surrender 

Surrender 

Surrender 

Surrender 

Value. 

Charge. 

Value. 

Charge. 

Value. 

Charge. 

36 

O.OO 

17-33 

0.00 

13.26 

6.38 

437 

37 

5-S9 

17-45 

3-44 

13-45 

13-14 

8.74 

38 

18.02 

17-57 

12.31 

13-64 

20.29 

13-H 

39 

30-56 

17.69 

21.  6l 

13-S4 

27.84 

17-54 

40 

43-52 

I/.82 

3'-45 

14.05 

35-81 

21-95 

4i 

56.91 

17-95 

4I-5I 

14.27 

44-20 

26.36 

42 

70-75 

18.09 

52.24 

14.50 

53-03 

30.78 

43 

85.07 

lS.22 

63-39 

14-74 

62.30 

35-20 

44 

99-79 

18-37 

75-H 

14.98 

72.04 

39.62 

45 

114.90 

iS.si 

87.27 

l.S-23 

82.23 

44-03 

46 

130-37 

iS.6s 

99.80 

15.48 

92.90 

48.42 

47 

146.14 

18.78 

112.77 

15-73 

104.03 

52-79 

48 

162.21 

18.90 

126.12 

15.98 

115.64 

57-  1  2 

49 

i/S-55 

19.01 

I39-83 

l6.  21 

127.72 

61.40 

5° 

I95-I9 

19.11 

1^4.01 

16.45 

140.25 

65.62 

51 

212.07 

19.21 

168.50 

16.68 

153-23 

69.76 

52 

229.22 

19.28 

183-31 

16.89 

166.66 

73.80 

53 

246.57 

19-35 

198.50 

17.10 

180.54 

77.72 

54 

264.14 

19.40 

214.13 

17-30 

194.84 

Si-53 

55 

281.92 

J9-43 

230.01 

17-49 

209.57 

85.18 

56 

299.87 

19-45 

246.23 

17-67 

224.71 

88.68 

57 

3  '7-98 

19-45 

262.68 

17.82 

240.24 

92.00 

58 

33^-25 

19.44 

279-53 

17.97 

256.16 

95-13 

59 

354-65 

19.41 

296.75 

18.10 

272.46 

98.03 

60 

373-iS 

19-35 

3  14-11 

lS.2I 

289.10 

100.73 

61 

39-  /3 

19.29 

33I-65 

18.30 

306.07 

103.18 

62 

4  '0-33 

19.19 

3-19-43 

lS-37 

323-34 

105-37 

63 

428.90 

19.08 

367-38 

18.42 

340.89 

107.30 

64 

447-42 

18.94 

3S4-5I 

18.44 

358.71 

108.93 

65 

465-85 

18.79 

403-56 

18.44 

3/6-74 

110.29 

66 

484.17 

18.60 

421-59 

18.41 

394.96 

m-3 

67 

50^.32 

18.40 

439-  M 

18.36 

4I3.34 

112.06 

68 

520.29 

18.16 

457-93 

lS.27 

43'  -84 

112.46 

69 

538-04 

17.91 

4/5-84 

18.16 

450.42 

112.52 

ENDOWMENT  POL.  OF  $1.000,  ENTERED  AT  35.  PAYABLE  AT  45  OR  PREVIOUS  DEATH. 

Actual  Prem.,  $105.58 

Actual  Prnn..  $89.25 

Actual  Prem.,  $io<;  .53. 

Net  Prem.,  $85.03. 

Net  Prem.,  $76.71. 

Net  Prem..  $84.80. 

36 

77.19 

2.72 

70.05 

2.65 

72.49 

7-47 

37 

161.38 

-2.22 

148.13 

2.18 

149.92 

13.82 

38 

249-57 

1.74 

23I-47 

i-74 

232.67 

18.90 

39 

342.00 

1-30 

320.47 

1.32 

32'-I3 

22.51 

40 

438.77 

.92 

4I5-57 

•93 

4I5-74 

24.47 

4i 

540.48 

.58 

517-24 

•58 

5I6.97 

24-5* 

42 

647.10 

•30 

625.92 

•32 

625-38 

22.46 

43 

758.99 

.11 

742.21 

.11 

741-55 

17.92 

44 

876.51 

.00 

866.68 

.00 

866.17 

io-55 

45 

1,000.00 

.00 

1,000.00 

.00 

I.OOO.OO 

0000 

156  OF  LIFE  INSURANCE. 

VALUATION  OF  JOINT-LIFE  POLICIES. 

BY  SETH  C.  CHANDLER,  JR., 

Actuary  of  the  Continental  Life  Insurance  Company,  of  N.  T. 
The  following  simple   modification  of  the    "accumulation" 
formula  offers  peculiar  facilities  for  the  valuation  of  all  kinds  of 
joint-life  and  joint-endowment  policies,  though  its  application  is 
by  no  means  limited  to  this  class  of  insurances,  but  is  universal. 
By  substituting  the  values  of  u  and  k, 


r 


in  the  "  accumulation"  formula, 

n  +  !  71 

Hxy  =  «xy  +  n  (Hxy  +  **»)   ~ 

we  obtain  the  expression, 


where  pxy+n  is  the  probability  of  two  lives  x+n  and  y+n  or 
the  product  of  the  probabilities  of  each  life  living  one  year. 

This  formula  dispenses  with  the  necessity  for  the  preparation 
of  the  auxiliary  quantities  u  and  k  for  different  combinations  of 
ages,  and  requires  simply  a  table  of  the  arithmetical  complements 
of  the  logarithms  of  the  probability  of  living  one  year. 

The  values  of  this  element,  according  to  the  Actuaries' 
table  of  mortality,  are  here  inserted,  and  also  an  example  of  the 
method  of  computation  by  the  formula. 

Example.  Required,  the  net  values  by  the  "  actuaries'  "  table 
4  per  cent  interest  at  the  end  of  the  first  and  second  years,  of  an 
ordinary  joint-life  policy  issued  at  ages  46  and  38. 
TT  46-38  =-----------    .041036 

TT  46-38  xi.  04  =---------        .042677 

^(TT  46-38  xi.  04)  =   .........    -957323 

i-(7r46-3Sxi.o4)  x-^-x—  ^-  =        .....         -979477 

H'46-38  —     .....        ......    .020523 

Second  year.  — 
1^46-38  +  ^46-38   =---.,        .....          -061559 

x  1.04  =-----------     .064021 

i  —  (H  '46-38  +  ^46-38)  i.  04  =     .......         -935979 

xx?k"    .........  -958514 

..........         .041486 


PRINCIPLES  AND  PRACTICE 


'57 


TABLE  No    LXI      • 

VALUATION   OF  JOINT-LIFE    POLICIES,    CHANDLER'S  FORMULA,    COM- 
BINED EXPERIENCE,  4  PER  CENT. 


Age. 

^og.~ 

I 

7 

Age. 

Log.- 

i 
P 

10 

002.9458 

i.  0068  i 

48 

006.2374 

.01447 

II 

002.9571 

1.00683 

49 

006.5907 

.01529 

12 

002.9685 

1.00686 

50 

006.9798 

.01620 

13 

002.9845 

1.00690 

51 

007.4015 

.01719 

«4 

003.0052 

1.00694 

52 

007.8652 

.01828 

IS 

003.0260 

1.00699 

53 

008.3720 

.01946 

16 

003.0519 

1.00705 

54 

008  9128 

.02073 

17 

003.0781 

1.00711 

55 

009.5121 

.02215 

18 

003.  1092 

1.00718 

56 

010.1615 

.02367 

19 

003.1410 

1.00726 

57 

010.8526 

•02530 

20 

003.1780 

1-00735 

53 

011.6130 

.02710 

21 

003.2156 

1.03743 

59 

012.4439 

.02907 

22 

003.2538 

1.00752 

60 

013.3788 

.0^128 

2.3 

003  2976 

1.00762 

61 

014.3991 

*  -0337  i 

24 

0033421 

1.00773 

62 

015.5269 

1.03640 

25 

003.3876 

1.00783 

63 

016.7526 

1-03943 

26 

0034387 

1.00795 

64 

018.1024 

1.04256 

27 

003.4910 

1.00807 

65 

019-5793 

1.04611 

28 

003.5491 

1.00821 

66 

021.1869 

1.04999 

29 

003.6087 

1.00834 

67 

022.9508 

1.05427 

3° 

003.6743 

1.008^9 

68 

024.8578 

.05891 

31 

003.7416 

1.00865 

69 

026.9124 

•06393 

3^ 

003.8154 

1.00882 

70 

029.1572 

•06944 

33 

003.8909 

1.00900 

7i 

03  i-  59°9 

•07545 

34 

003.9682 

1.00918 

72 

034-2363 

.08202 

35 

004.0525 

1.00937 

73 

037.1022 

.08919 

36 

004.1389 

1.00957 

74 

040.2280 

.09700 

37 

004.2274 

1.00978 

75 

043.6203 

.10566 

33 

004.3237 

I.OIOOI 

76 

047.2944 

•"505 

39 

004.4223 

1.01024 

77 

051-3275 

•12545 

40 

004.5236 

1.01047 

78 

055-7367 

.13694 

4i 

004.6333 

.01073 

79 

060.5131 

•M95* 

42 

004.7573 

.01101 

So 

065.7068 

•16334 

43 

004.9139 

.01136 

Si 

071.3152 

.17846 

44 

005.1100 

.01186 

82 

077-375I 

.19502 

45 

005.3363 

.01234 

83 

084.0265 

.21346 

46 

005.6120 

.01301 

84 

091.3426 

.23408 

47 

005.9098 

.01370 

85 

099.6848 

.25801 

158  PRINCIPLES.  AND  PRACTICE 

A  NEW  METHOD  OF  VALUING  POLICIES. 

BY  EMORY  MCCLINTOCK, 
Actuary  of  the  Northwestern  Mutual  Life  Insurance  Company,   Wis. 

The  following  formula;  for  valuing  whole  life  policies  and 
endowment  policies  premiums  payable  to  a  certain  age,  is  now 
published  for  the  first  time,  and  for  one  who  has  not  the  valua- 
tion tables  at  hand,  is  the  easiest  method  of  finding  the  reserve 
on  a  policy  at  the  end  of  the  year. 

Having  graded  the  column  of  "  differences"  according  to  the 
space  given  for  the  table,  the  "values"  are  found  by  the  follow- 
ing formula. 

Let  d •=  the  difference. 

"Value"  =  looo  [i — log-1  (o — oooi  x  d)  ] 

Example.  Let  d  =  500,  required  the  "  value." 

1,000  [i— log-1  (o— ooo  i  x  500)]  =  i, ooo  [i— log-1  (0—005)]== 

1,000  [i—  log"1  (9,9950000)]  =  i,ooox  (i — 9SS55)  =  n.45. 

.98855  is  the  nearest  number  corresponding  to  log.  9,9950000. 

Let  d  =  4000,  required  the  "  value." 

1,000  [ i— log"1  (0,0000 1  x  40oo)]  =  icoo  [i—  log"1  (0.04)]  = 

1,000  x  i  —log"1  (9,960  0000)  =  i  ooo  x  (i—  .91201)=  87. 99. 

This  table,  which  is  simply  one  of  the  complements  of  loga- 
rithms, and  the  complements  of  numbers  corresponding  to  these 
complements,  applies  to  all  the  intermediate  values  of  d,  and  to 
any  table  of  mortality  and  rate  of  interest. 

The  "  age  numbers"  in  this  table  for  whole  life  policies,  were 
obtained  by  the  formula,  100,000  (log.  A  15  —  log.  A  15+  »/), 
and  the  general  formula  is  100,000  [log.  Ax—  log.  Ax+m),  m 
denoting  the  year  of  the  policy  in  which  the  value  is  required. 

The  formula  for  "  age  numbers  "  on  endowments  issued  at 
age  *,  and  payable  at  age  x  +  n,  is 

100,000  Hog-     *~    x+n  —log.  — ~m — ±±*\ 

x  '  "*"  m         ' 

Examples  of  finding  the  value  of  a  policy  by  this  method. 

Required  the  value  of  a  whole  life  policy,  age  30,  at  the  end 
of  the  3d  year.  American  Experience  4^  per  cent. 

Under  the  column  of  "  age  numbers"  of  whole  life  policies 
opposite  age  30,  is  the  age  number  3,476  ;  opposite  33,  the  age 
at  valuation,  it  is  4,531,  and  the  difference  of  these  "  age  num- 
bers" is  1,055.-  By  inspecting  the  column  of  "  differences,"  we 


OF  LIFE  INSURANCE. 


159 


find  the  value  opposite  to  1,000  to  be  22.76,  and  the  difference 
between  1,055  ant^  !jOOO  multiplied  by  the  "  multiple  of  differ- 
ence" 2.25,  gives  55  x  2.25  =  1.23,  which  added  to  22,76,  gives 
22.76  +  1.23  =  23.09,  the  value  required. 

Required  the  value  of  the  same  policy  at  the  end  of  the  loth 
year. 

The  age  number  at  40  is  7,700,  and  at  36  is  3,376,  difference 
of  age  number  4,224  ;  value  opposite,  4,200  =  92.18,  corrections 
4,224—4,200  =  24  x  2.09  =50,  therefore  92.18  +  50  =  92,88,  the 
value. 

Required  the  value  of  an  endowment  policy,  age  20,  3d  year, 
payable  at  death  or  40.  American  Experience,  4*  per  cent. 

The  difference  in  the  age  numbers  in  the  column  "  Death,  or 
40,  is  9,426—5,188  =  4,238  ;  value  opposite  4,200  =  92.18,  cor- 
rection (4,238—4,200)  2.09  =  So  ;  therefore  92.18  +  So  =  92,98, 
the  value. 

This  method  of  valuation  applies  only  to  the  terminal  values 
of  whole  life  policies  and  to  continued  premium  endowments 
maturing  at  certain  ages,  but  the  values  of  nearly  all  continued 
premium  endowments  can  be  found  by  this  table  in  the  suffi- 
cient exactness  for  all  practical  purposes.  Thus  the  reserve  on 
a  ten  year  endowment,  age  43,  payable  at  death,  or  53,  differs 
but  very  little  from  the  reserve  on  an  endowment  issued  at  45 
and  payable  at  55. 

With  a  little  practice,  the  terminal  value  of  any  policy  given 
in  these  tables  can  be  found  to  the  nearest  dollar  by  inspection. 


i6o 


PRINCIPLES  AND    PRACTICE 
TABLE   NO.   LXII. 


VALUES  AND  DIFFERENCES  FOR  MCCLINTOCK'S  METHOD  OF  VALUING 
POLICIES,  ADOPTED  TO  ANY  TAIILE  OF  MORTALITY  AND  RATE  OF 
INTEREST. 


Difference. 

Value. 

Multiple  of 
Difference. 

Difference. 

Value. 

Multiple  of 
Difference. 

.IOO 

$2.30 

2.29 

5.100 

$110.80 

2.04 

.2OO 

4-59 

2.29 

5-200 

112.84 

2.04 

.303 

6.SS 

2.29 

5-300 

11488 

2.04 

.400 

9.17 

2.28 

5.400 

116  92 

2.03 

./JOO 

"•45 

2.27 

5-5°0 

11895 

2.03 

.Coo 

13.72 

2.27 

5.600 

20-98 

2.02 

.700 

15-99 

2.26 

5.700 

23.00 

2.  02 

.800 

18.25 

2.l6 

5.800 

25.02 

2.OI 

.900 

20.51 

2-25 

5.900 

27.03 

2.01 

I.OOO 

22.76 

2.25 

6.000 

29.04 

2.OO 

.100 

25.01 

2.24 

6.2CO 

33-°4 

•99 

.200 

27-25 

2.24 

6.400 

137.02 

.98 

.300 

29.49 

2-23 

6.600 

140.99 

•97 

.400 

3i-72 

2.23 

6.800 

M4-93 

•97 

.500 

33-95 

2.22 

7  ooo 

148.86 

.96 

.600 

36.17 

2.22 

7.200 

i52-77 

•95 

.700 

3S-39 

2.21 

7.400 

156.67 

1.94 

i.Soo 

40  60 

2.21 

7.600 

160.54 

1-93 

1.900 

42.81 

2.20 

7.800 

164  4O 

1.92 

2.OOO 

45.01 

2.19 

8.  ooo 

I6S.24 

1.91 

2.  IOO 

47.20 

2.19 

8.200 

I72.0(j 

1.90 

2.200 

49.40 

2.18 

8.400 

175.86 

1.89 

2-300 

5i-5S 

2.18 

8600 

I79-65 

1.88 

2.400 

53-76 

2.18 

8.800 

183.^2 

1.87 

2.SOO 

55-94 

2.17 

9.000 

l87.I7 

i.  86 

2.600 

58.11 

C.17 

9.200 

I9O.9O 

i.  86 

2.7OO 

60.28 

2-l6 

9400 

I9J.62 

1-85 

.Soo 

62.44 

2-15 

9.600 

19^-32 

1.84 

2.900 

64-59 

2-15 

9.800 

202.  OI 

1-83 

3.000 

6675 

2.14 

10.000 

205.67 

1.82 

3.100 

68.89 

2.14 

IO.2OO 

209.32 

i.Si 

3.200 

7i-c>3 

2.14 

10  400 

21295 

i.Si 

3-300 

73-'7 

2-13 

10.600 

216.57 

i.So 

3.400 

75-30 

2.12 

10  Soo 

220.17 

1.79 

3.500 

77-43 

2.12 

11.  OOO 

223-75 

1.78 

3.600 

79-  '5 

2.  1  1 

II.2OO 

227.32 

i-77 

3.700 

81.67 

2.11 

11.400 

230.87 

1.76 

3  ^0° 

83.78 

2.11 

1  1  .600 

234-40 

1.76 

39~o 

85.89 

2.IO 

11.800 

237-92 

i-75 

4.003 

87.99 

2.IO 

12.000 

241.42 

1.74 

4.100 

90.09 

2.O9 

12.200 

244.91 

1-73 

4  200 

92.18 

2.09 

12  400 

248.38 

1.72 

4.300 

94.27 

2.o8 

I2.6OO 

25I-«3 

1.72 

4.400 

90-35 

2.08 

12.800 

255-27 

1.71 

4.500 

98-43 

2.07 

13  ooo 

258  69 

1.70 

4.600 

100.50 

2.O7 

13.200 

262.10 

1.69 

4.700 

102.57 

2.06 

13.400 

261  49 

1.68 

4.800 

104.63 

2.  (.6 

13  600 

268.86 

i.  68 

4.900 

106.69 

2.06 

13-SoO 

272.22 

1.67 

5.000 

10875 

2.05 

14.000 

275-56 

1.66 

OF  LIFE  INSURANCE. 


161 


TABLE   No.  LXII.— (CONTINUED.) 

VALUES  AND  DIFFERENCES  FOR  MCCLINTOCK'S  METHOD  OF  VALUING 
POLICIES,  ADOPTED  TO  ANY  TABLE  OF  MORTALITY  AND  RATE  OF 
INTEREST. 


Difference. 

Value. 

Multiple  of 
Difference. 

Difference. 

Value. 

Multiple  of 
Difference. 

14.200 

278.89 

1.66 

25-a50 

440.89 

1.28 

14.400 

282.21 

1.65 

25-500 

444.10 

1.27 

14.600 

285.50 

1.64 

25-750 

447-29 

1.27 

14.800 

288.79 

1-63 

26.000 

450.46 

1.26 

15.000 

292.06 

1.62 

26.250 

453-61 

1.26 

15.200 

29.v3I 

1.61 

26.500 

456.75 

1.25 

15400 

298.54 

1.61 

26.750 

459-87 

1.24 

15.600 

301.77 

i.  60 

27.000 

462.97 

1.23 

15.800 

304.98 

1-59 

27.250 

466.05 

1.22 

l6.OOO 

308.17 

1-58 

27.500 

469.12 

1.  21 

I6.2OO 

3"-35 

I-5S 

27.750 

472.16 

1.  21 

16.400 

3H-51 

1-57 

28.000 

475.I9 

1.  2O 

16.600 

317.66 

i-57 

28  250 

478.20 

1.20 

16.800 

320.80 

1-56 

28.500 

481.20 

I.I9 

17.000 

323.92 

i-55 

28.750 

484.18 

i.iS 

17.200 

327.02 

i-55 

29.000 

487.14 

1.18 

17.400 

330.12 

1-54 

29.250 

490.08 

1.17 

17.600 

333-19 

i-53 

29.500 

493.01 

1.16 

17.800 

336.26 

1.52 

29.750 

495.92 

i-i5 

18.000 

339-31 

i-5i 

30.000 

498.81 

I-I5 

18.200 

342-34 

i-5i 

30.250 

501.69 

1.14 

18.400 

345-36 

1.50 

30.500 

504-55 

1.14 

18.600 

343-37 

1.50 

30.750 

507-39 

i-i3 

18.800 

351-37 

1.49 

3I.OOO 

510.23 

1.  12 

ig.OOO 

354-35 

1.48 

3I-250 

5I3-03 

1.  12 

19.200 

357-31 

1.48 

31-500 

515-83 

I.  II 

19.400 

360.27 

1.47 

3J-750 

518.61 

1.  10 

19.600 

363.20 

1.46 

32.000 

521-37 

1.  10 

19.800 

366.13 

i-45 

32.250 

524.12 

1.09 

20.00O 

369.04 

i-45 

32-500 

526.85 

1.08 

20.250 

372.66 

1.44 

33-ooo 

532.26 

1.07 

20.500 

376-27 

i-43 

33-500 

537-62 

1.  06 

20.750 

379-84 

1.42 

34.000 

542.91 

1.05 

21.000 

383-40 

1.41 

34-500 

548.14 

1.04 

21.250 

386.94 

1.41 

35-000 

553-32 

1.  02 

21.500 

390.46 

1.40 

35-500 

558.43 

1.  01 

21.750 

393-96 

i-39 

36.000 

563.48 

I.OO 

22.OOO 

397-44 

1.38 

36.500 

568.48 

•99 

22.250 

400.90 

i-37 

37.000 

573-42 

.98 

22.500 

404-34 

i-37 

37-550 

578.30 

•97 

22.750 

407.76 

1-36 

38.000 

583.13 

.96 

23.000 

411.16 

i-35 

38.500 

587.90 

•95 

23.250 

4H-54 

•34 

39.000 

592.62 

•94 

23.500 

417.90 

•33 

39-500 

597-28 

.92 

23-750 

421.24 

•33 

40.000 

601.89 

.91 

24.000 

424.56 

•32 

40.500 

606.45 

.90 

24.250 

427.86 

•3i 

41.000 

610.95 

.90 

24.500 

43I-I5 

•30 

41.500 

615.41 

.89 

24-750 

43441 

•30 

42.000 

619.81 

.88 

25.OOO 

437-66 

.29 

42.500 

624.16 

.87 

162 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LXIL— (CONTINUED.) 

VALUES  AND  DIFFERENCES  FOR  ^'CCLINTOCK'S  METHOD  OF  VALUING 
POLICIES,  ADOPTED  TO  ANY  TABLE  OF  MORTALITY  AND  RATE  OF 
INTEREST. 


Difference. 

Value. 

Multifile  of 
Difference. 

Difference. 

Value. 

Multiple  of 
Difference. 

43.000 

$628.46 

.86 

68.000 

$791.07 

.48 

43-  5°° 

632.72 

•85 

68.500 

793-46 

•47 

44.000 

636.92 

•83 

69.000 

795-83 

•47 

44.500 

641.08 

.82 

69.500 

798.  16 

.46 

45.000 

645-19 

.81 

70.000 

800.47 

.46 

45.500 

649.25 

.80 

70.500 

802.76 

•45 

46.000 

653-26 

•79 

71.000 

805.02 

•45 

46.500 

657-23 

.78 

71.500 

807.25 

•44 

47-000 

661.15 

.78 

72  coo 

809.45 

•44 

47.500 

66v03 

•77 

72.500 

811.64 

•43 

48.000 

688.87 

•76 

73-ooo 

813-79 

•43 

48.500 

672.66 

•75 

73-500 

815.92 

.42 

49.000 

676.41 

•74 

74.000 

818.03 

.42 

49.500 

680.  1  1 

•73 

74.500 

820-11 

.41 

5O.OOO 

683-77 

•72 

75-000 

822.17 

.41 

50.500 

687-39 

•72 

75-5eo 

824.21' 

.40 

51.000 

690.97 

•7i 

76.  dcJo  • 

826.22 

.40 

5*-5*i 

694-5I 

.70 

76.500 

828  21 

•39 

52.000 

698.00 

.69 

77.000 

830.18 

•39 

52-5oo 

701.46 

.68 

77-500 

832.12 

•38 

53.006 

704.88 

.68 

78.000 

834.04 

•38 

53-5oo 

708.26 

.67 

78.500 

835-94 

•38 

54.000 

711.60 

.66 

79.000 

837-82- 

•37 

54-  SCO 

714.90 

•65 

80.000 

841.51 

•36 

55.000 

718.16 

•65 

81.000 

845.12 

•35 

55-  5°° 

721-39 

.64 

82.000 

848.64 

•35 

56.000 

724.58 

•63 

83.000 

852.09 

•34 

56.500 

727-73 

.62 

84.000 

855-46 

•33 

57.000 

730-85 

.62 

85.000 

858.75 

•32 

57-50° 

73393 

.61 

86.000 

861.96 

•3i 

58.000 

73697 

.60 

87.000 

865.10 

•3i 

58  5°° 

7399s 

•59 

88.000 

868.17 

•30 

59.000 

742.96 

•59 

89.000 

871.18 

.29 

59-500 
60.000 

745-90 
74881 

•58 
•58 

90.000 
91.000 

874.11 
87697 

.286 
.280 

60.500 

751-69 

•57 

92,000 

87977 

.270 

61.000 

754-53 

•56 

94.01.0 

885.18 

•259 

61.500 

75734 

•56 

96.000 

890-35 

•247 

62.000 

760.12 

•55 

98.000 

895.29 

.236 

62.500 

762.86 

•54 

IOO.OOO 

900.00 

.225 

63.000 

765-58 

•54 

IO2.OOO 

904.50 

•215 

63-5CO 

768.26 

•53 

104.000 

908.80 

.205 

64.000 
64.500 

770.91 

77354 

•53 

•52 

106  ooo 
108  ooo 

912.90 

916.82 

.196 

.188 

s~ 

65.000 

7/6-13 

•51 

no  ooo 

920.57 

.163 

65.500 

778.69 

•5i 

I2O.OOO 

936.90 

.130 

66.000 

781.22 

•50 

130.000 

949.88 

.103 

66.500 

783-73 

•49 

140.000 

960.19 

.082 

«.^C  rf 

67.000 

786.20 

-49 

150.000 

968.38 

.065 

67.^00 

788.65 

.48 

1    160.000 

974  88    i         .050 

OF  LIFE   INSURANCE. 


163 


TABLE  No.  LXIII. 

McCLiNTOCK's   METHOD  OF  VALUING    POLICIES;    JOINT  LIVES,   AGE 
NUMBERS,  COMBINED  EXPERIENCE,  4  PER  CENT. 


Tottno'tr 
Age. 

Equal 
Ages. 

2>/y.  »V» 

vl^YS, 

5   JVars. 

J9/^".  in 
Ages, 
10  tears. 

Diff.  in 
Age*. 
15  1  ears. 

Diff.  in 
Agts. 
2O  /  ears. 

Diff.  in 
Ages, 
25  tears. 

Diff.  in 
Ages, 
30  Tears. 

15 

.000 

.OOO 

.OOO 

.OOO 

.000 

.000 

.OOO 

16 

.269 

.302 

•346 

•405 

.487 

.604 

•753 

17 

•550 

.616 

.706 

.828 

.996 

1.239 

i-536 

IS 

.842 

•943 

1.  08  1 

1.269 

I-53° 

1.906 

2-350 

19 

I.I47 

1.284 

1.471 

1.729 

2.089 

2.6os 

3-195 

20 

1.464 

1.639 

1.879 

2.210 

2.676 

3-336 

4-073 

21 

i-794 

2.008 

2-305 

2.713 

3.291 

4.097 

4-985 

22 

2.138 

2-393 

2.748 

3-238 

3-938 

4.887 

5-931 

23 

2.496 

2-794 

3-210 

3-788 

4.617 

5-711 

6.  112 

24 

2.868 

3-212 

3.691 

4-363 

5-328 

6.565 

7.928 

25 

3-256 

3-647 

4.194 

4966 

6.071 

7.451 

8-983 

26 

3.660 

4.101 

4-7r9 

5-599 

6-845 

8.371 

10.073 

27 

4.080 

4-573 

^.268 

6.264 

7.649 

9.326 

11.207 

28 

4-5I9 

<5-o66 

5-843 

6.962 

8.485 

10.316 

12.381 

29 

4.976 

5-581 

6-444 

7.692 

9-353 

11.342 

I3-598 

30 

5-452 

6.1  18 

7-074 

8-455 

10.255 

12.406 

14.858 

3.1 

5-94S 

6.678 

7-73-5 

9.251 

11.189 

13.509 

I&I& 

32 

6.466 

7:264. 

8,429 

10.077 

12.159 

14.65-1 

17-:  soft; 

33 

7.006 

7.:S7S 

-   9-lST 

10.936 

13-165 

15.835 

I&S9J 

34 

7-569 

8.520 

9.920 

11.827 

14.208 

17.062 

20-3^4> 

35 

8--  1  59 

9,192. 

10.718 

12.754 

15.290 

18.334 

.2J.797T 

36 

8-775 

9.900 

"•550 

13-717 

16413 

19.650 

23-313 

37 

9-42J 

10.644 

12.415 

14.717 

I7-576 

21.009 

24.870. 

38 

10.098 

11.425 

J3-3'7 

15-757 

18.784 

22.413 

26.470 

39 

10.808 

12.246 

14-255 

16.836' 

20.038 

23.862. 

28.113 

40 

"•555 

13-105- 

I5-233 

17-958 

21.340 

25-356 

29.800 

4i 

12.342 

14.005 

16.252 

19.124 

22.490 

26.896 

31-533 

42 

13.171 

14-944 

17-313 

20-337 

24.088 

28.484 

33-312 

43 

14.046 

15.926 

18.419 

21.600 

25-535 

30.117 

35-I38 

44 

14.963 

16.948 

19.569 

22.912 

27.030 

31-795 

37-oi2 

45 

15.922 

18.012 

20.763 

24.272 

28.572 

33-519 

3S-939 

46 

16.922 

19.116 

22.OOI 

25-679 

3°-I58 

35.288 

40.894 

47 

I7-958 

20.259 

23.281 

27.131 

31.786 

37.098 

42.902 

48 

19.032 

21-443 

24.606 

28.627 

33-456 

38.950 

44954 

49 

20.144 

22.667 

25-977 

30.  166 

35  '66 

40.845 

47.047 

50 

21.297 

23-934 

27-394 

,o   o  -  - 

3L750 

36-919 

ryQ    H  f  A 

42.781 

A  A    *j(yCl 

49.186 

51 

22.490 

25.244 

20.857 

33-376 

3i3-7I4 

44.700 
Aft  787 

53 

23-725 

26.597 

30-364 

35.O45 

4O-551 

At   /nQ 

4°"  /°J 

AS  SAH 

53 

25.000 

^/r    -  T  Q 

27.966 

31.916 

36-754 

Oo   -.  ,  . 

42.420 

40.047 

r  f\  f\c  2 

54 

26.310 

/**    AQ  T 

29.441 

33-512 

3a-5°4 

44-347 

A  f\  "?ri*7 

5U<95^ 

C7    TOO 

55 
-f. 

27.001 
«~  ,-.00 

3°-935 

35-  152 

->fi  Q-jr 

40.296 

40.307 

5V5-1L*J 

5" 

29.000 

32-474 

3°-&35 

,q  rf.r 

42.130 

3 

30.540 

3-1  -°59 

30.501 

44.005 

A  C    nT} 

5° 

32.041 

35-691 

4°-33° 

45-9  2* 

A>7    SS-> 

59 

f<n 

33-592 

37-371 

42.142 

A  f  f\r& 

47.002 
An  8S? 

VJ*J 

it* 

35-H9 
tf\  R/i? 

39.097 

*r*i  9A-T 

43.990 

49.00.5 

wi 
flf 

3°-°43 

,C    ,,Q 

40.  007 

\J& 

f.-. 

3o-53° 

Ar\   >*?S 

42.679 

A  4     T"?  T 

°3 

f>A 

tfU.  —  /  O 

44o3x 

°4 

42.O62 

•^  '  *  .  |  j  j 

164 


PRINCIPLES  AND  PRACTICE 


TABLE  No  -  LXIV. 

MCCLINTOCK'S  METHOD  OF  VALUING   POLICIES,  AGE  NUMBERS, 
AMERICAN   EXPERIENCE,  4^  PER  CENT. 


Age. 

Whole  Life. 

Endotvmtnt  at 
Death,  or  40. 

Endoivmtnt  at 
Death,  or  45. 

J5nifo7vmfttl  at 
Death,  or  50. 

15 
16 

17 

18 

'9 

20 
21 
22 
23 
24 
25 
26 

27 
28 

29 
30 
31 
32 

33 
34 

3I 
36 

37 

38 

39 
40 

4i 
42 
43 
44 
45 
46 

47 
48 
49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 

8 

60 

61 

62 

63 
64 

.OOO 

.i6j 
•332 

•5'i 
.698 

•895 

Z.IOI 

i-3i7 

1-544 
1.781 
2.030 
2.292 
2.567 
2-855 
3-I58 
.  3-476 
•     3-Sii 
4.162 

4-531 
4.919 
5-326 

5-755 
6.205 
6.679 

7-177 
7.700 
8.250 
8.829 

9-438 
10.079 
10.752 
11.460 
12.204 
12.985 
13.804 
14.662 

15-559 
16.497 

17-477 
18.501 
19.568 
20.681 
21.839 
23.046 
24.301 
25.605 
26.959 
28.364 
29.821 
3i-33o 

.OOO 
.891 
1.^48 
2.878 

3-987 
5.188 
6.486 
7-884 
9.426 
11.098 
12.929 
14.944 
17.169 
19.642 
22.405 
25-518 
29-055 

33-120 
37-856 
43-475 
50-304 
58893 
70.271 
86.750 
115.708 

.OOO 
.638 

I-3I9 
2.047 
2.825 
3-658 
4-551 
5-510 
6.541 
7.652 
8.852 
10.150 
11-558 
13.090 
14.762 
16.592 
18.605 
20.829 
23.298 
26.058 
29.166 
32.697 

36-755 
41.483 
47.091 

53-9'J8 
62.482 

73-843 
90.301 

119-235 

.000 

.472 

•973 
1.506 
2.072 
2.675 
3-3i8 
4.003 
4-734 
5-5I5 
6-352 
7.248 

8.210 

9.244 
10-358 
11.560 
12.860 
14.271 
15.804 
17.476 
19.306 
21.319 
23-540 
26.006 
28.762 
31-863 
35-386 

39-433 
44.148 
49.741 
56.538 
65.089 
76.42! 
92844 
121-735 





OF  LIFE  INSURANCE. 


I65 


TABLE  No.  LXIV.— (CONTINUED.) 

McCLiNTOCK's   METHOD  OF  VALUING   POLICIES,   AGE  NUMBERS, 
AMERICAN  EXPERIENCE,  4^  PER  CENT. 


Ag*. 

Endowment  at 
Death,  or  55. 

Endowment  at 
Death,  or  60. 

Endowment  at 
Death,  or  65. 

Endowment  at 
Death,  or  70. 

15 

.COO 

.OOO 

.OOO 

.OOO 

16 

•357 

.282 

.230 

.197 

17 

•757 

•579 

.472 

•403 

18 

I-I39 

•893 

.670 

.621 

19 

1-565 

1.225 

.996 

•849 

20 

2.017 

1-575 

1.279 

1.090 

21 

2.496 

1.946 

l'57& 

1-343 

22 

3.004 

2-337 

1.892 

i.  608 

23 

3-544 

2-751 

2.223 

1.  888 

24 

4.117 

3-189 

2-573 

2.182 

25 

4.727 

3652 

2.942 

2.491 

26 

5-377 

4.144 

3332 

2.817 

27 

6  609 

4.665 

3-743 

3.161 

28 

6.808 

5.218 

4*79 

3-522 

29 

7-597 

5.806 

4.638 

3-904 

3° 

8.440 

6.430 

5-125 

4.306 

3i 

9-344 

7.094 

5.640 

4730 

32 

10.313 

7.801 

6.186 

5-I78 

33 

H355 

8-555 

6.764 

5-65I 

34 

12-475 

9259 

7378 

6.151 

35 

13684 

10.218 

8.029 

6.679 

36 

14.990 

11.138 

8.722 

7-237 

37 

16.406 

12.123 

9-458 

7.828 

3S 

17-944 

13.180 

10.242 

8.453 

39 

19.620 

14.316 

11.076 

9.114 

40 

21-453 

15-540 

11.967 

9.816 

41 

23.466 

16861 

12.917 

10-559 

42 

25.688 

18.290 

13-934 

11.348 

43 

28.152 

19841 

15-023 

12.186 

44 

30-903 

21.529 

16.191 

I3-077 

45 

3399s 

23373 

17-447 

14.025 

46 

37-5" 

25-395 

18.800 

I5-034 

47 

41-544 

27.621 

20.259 

16.110 

48 

46.240 

30.088 

21.837 

17-257 

49 

51.808 

32-835 

23-549 

18.483 

50 

58.572 

35-920 

25.412 

19.792 

5' 

67.079 

394H 

27-445 

21.193 

52 

78.356 

43.418 

29.675 

22.695 

53 

94.711 

48.074 

32.135 

24.309 

52 

123.521 

53-588 

34876 

26.049 

re 

60  78  c 

7*7  0^2 

27  Q1O 

OJ 

r<5 

*J\J*  ^O^ 

68.710 

o/-y-* 

4.1    lid. 

*/  'yjr* 

2Q  O72 

o" 

C7 

79.886 

Ti-  O/T 
4C    722 

*y  71 
72   IOQ 

Jt 
rk 

06    T27 

45-0^* 
A(\  OO7 

o^-^W 
74.  6j.2 

O° 
CO 

yU.l.ij 
T  24  7OO 

TV-V^a 

CC  724. 

OT""T- 
77,  -142 

2y 

60 

i^T-/yj 

J.V  J^T 

61.906 

O/  -JT* 
4O.7.48 

61 

TO   IOI 

T^-'  JTV 
4.7  77O 

62 

/u.  iyi 
Sr  TOO 

T-  J  •  /  f* 

47.?8l 

61 

L»A>  j-yy 
OT  27C 

T/'.I'-'J 
C2  O47 

uj 
64 

y/'^JJ 
125.666 

O^-^TJ 

57-3" 

i66 


PRINCIPLES  AND  PRACTICE 


TABLE   No.    LXV. 

McCLiNTocK's  METHOD  OF   VALUING   POLICIES,   AGE  NUMBERS, 
COMBINED  EXPERIENCE  4  PER  CENT. 


Age. 

Whole  Life. 

Endowment  at 
Death,  or  40. 

Endowment  at 
Death,  or  45. 

Endowment  at 
Death,  or  50. 

15 
16 

17 

18 

19 

20 
21 
22 
23 
24 
25 
26 

27 
28 

29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 

AO 

.OOO 

.222 

•453 
.694 

•944 
1.205 
1.476 
1-758 
2.052 
2.358 
2.676 
3.607 
3-320 

3-7" 
4.085 

4-475 
4.8^1 

5-304 
5-745 
6.205 
6.6S6 

7.187 
7.711 
8.260 
8-833 

.OOO 

•973 
2.013 

3.128 

4-324 
5.609 

6.994 

8.490 

IO.II2 
11.874 

13-795 
15.901 

18.218 
20.782 

23.638 

26.842 

30-471 
34.628 
39-456 

45-  1  66 
52.086 
60.766 

72-234. 
88.803 
96.588 

.OOO 

•715 

1-473 
2.279 

3-137 
4-051 
5.026 
6.067 

7.182 

8-377 
9.661 
11.045 
12.538 
14.156 

I5-9H 
17.831 
19.930 
22.240 
24.994 
27.640 
30-832 
34.448 
38-590 
43-402 
49-095 

r  C.QQ7 

.OOO 

•543 
1.117 

1-723 
2.364 

3-043 
3-762 
4-525 
5-334 
6.195 
7.111 
8.087 
9.130 
10.245 
11.440 
12.724 
14.105 

I5-596 
17.210 
18.962 
20.873 
22.964 
25.266 
27.812 
30-647 
•n  S'o 

64.  6s6 

77  ,17,1 

*?6   IO7 

A  I    c6d. 

A1 

Q^^dS 

4.6.76.1 

107.716 

C2.O4.2 

rS  Q27 

45 

46 

67   CC7 

4U 

13*°v4 

78.960 

47 

A& 

OC.4.C7 

no  ccc 

49 

IO./45 

51 



52 

19*°93 

oJ 

54 

55 
c6 

5° 

-J3'391 

cA 

*4o°,> 

5° 
(a 

25'//° 

60 

^G   Tj-l 

6l 

*°»33J 

62 

67 

fiA 

04 
65 

.53-901 
35-475 

OF  LIFE  INSURANCE 
TABLE  No.  LXV.— (CONTINUED.) 


167 


MCCLINTOCK'S  METHOD  OF  VALUING  POLICIES;   AGE  NUMBERS, 
COMBINED  EXPERIENCE,  4  PER  CENT. 


Age. 

Endowment  at 
Death,  or  55. 

Endowment  at 
Death,  or  60. 

Endowment  at 
Death,  or  65. 

Endowment  at 
Death,  or  70. 

15 

.OOO 

.OOO 

.OOO 

.000 

16 

.426 

•346 

•293 

.258 

17 

•875 

.710 

•599 

.528 

18 

1-347 

I.ogi 

.920 

.810 

'9 

1.844 

I.49I 

I-255 

1.104 

20 

2.368 

I.gll 

1.606 

1.411 

21 

2.920 

2.351 

1.972 

I-73I 

22 

3-5°2 

2.814 

2-356 

2.065 

23 

4.116 

3-3°o 

2.758 

2.414 

24 

4-765 

3.810 

3-  '79 

2778 

25 

5-45  1 

4-348 

3.620 

3-159 

26 

6.177 

4-9'3 

4.082 

3-557 

27 

6.946 

5-5°9 

4-567 

3-973 

2S 

7.662 

6.138 

5.076 

4.408 

29 

8.629 

6.800 

5.611 

4-863 

30 

9-550 

7.500 

6.172 

5-339 

31 

10.532 

8.240 

6.762 

5-S38 

32 

n-579 

9.024 

7-383 

6.361 

33 

12.698 

9-853 

8.037 

6.908 

34 

13.896 

10-733 

8.726 

7-4S3 

35 

15.182 

11.669 

9-453 

8.087 

36 

16.565 

12.665 

IO.22I 

8.721 

37 

18.058 

13.726 

11.034 

9-388 

38 

19.674 

14.861      . 

11.895 

10.1-91 

39 

21.428 

16.075 

12.809 

10.832 

40 

23-34I 

17-379 

13.780 

ii  614 

4i 

25-436 

18.782 

14.813 

12.441 

42 

27.741 

20.296 

15.916 

i33J7 

43 

30.291 

21-934 

I7-093 

14.244 

44 

33-128 

23.710 

18.351 

1^-256 

45 

36.308 

25.641 

19.695 

16.263 

46 

39-9°3 

27-747 

2LI33 

17-359 

47 

44.013 

30-053 

22.673 

18.517 

48 

48.780 

3!-592 

24.327 

19.741 

49 

54-4H 

35-408 

26.109 

21.036 

50 

61.239 

38.556 

28.036 

22.412 

5i 

69.802 

42.109 

3°-I3° 

23-874 

52 

81.131 

46.167 

32.416 

25-43I 

53 

97-534 

50.872 

34.926 

27.0(98 

54 

"7-454 

56.43° 

37-702 

28.884 

cc 

6?  167 

J.O.7OO 

•30.806 

J.T 

r6 

uo*  lu/ 

•71   627 

T"  /  jfv 

44.2SS 

o 

32.886 

J> 

C7 

/  •«"•/ 

82.836 

^-(..    «<-JV-- 

48.  268 

7C    I  -l6 

Ji 

cS 

OO.  IOI 

C2  S7O 

O  -  '            T 

77.610 

ou 
CQ 

124  77O 

i>—  «**/;» 

c8."?2S 

JI  .'"V 

4.0.746 

3V 

60 

**T-  /  j" 

J^'J"^ 

f\A    O76 

T1^  OT 
41.77S 

61 

"T'V-J" 
TI.IA-I 

T*>    .>/ 

•i6.ciS7. 

62 

1  j"*tj 
8l  272 

•f^"  V    -J 

50.656 

6-1 

UT    *  / 

IOO.22s 

54.7^2 

64 

172  67s 

-IT      /     1 
6().O74 

UT 
65 

*.}*  "jj 

v                    /I 
66.^28 

1 68 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LXVI. 
VALUATION  COLUMNS. 


AMERICAN  EXPERIENCE,  FOUR  AND  A  HALF  PER  CENT. 

Aff€. 

«» 

Cm 

** 

A, 

15 

I-05304 

7-305 

7.692 

18.5509 

16 

I  -05307 

7-331 

7.720 

18.4818 

17 

1.05310 

7-357 

7.748 

18.4095 

18 

I-053H 

7-394 

7.786 

18.3339 

19 

1.05318 

7-43i 

7.826 

-18.2550 

20 

1.05322 

7-469 

7.826 

18.1726 

21 

1.05328 

7-5  i  7 

7.917 

18.0665 

22 

1-05333 

7.566 

7.969 

17.9968 

23 

I-05336 

7.616 

8.022 

17.9032 

24 

1-05344 

7.666 

8.075 

17-8055 

25 

I-05350 

7.717 

8.130 

17.7036 

26 

1  -05357 

7.780 

8.196 

17.5972 

27 

1.05364 

7.844 

8.264 

17.4862 

28 

I-0537I 

7.909 

8-333 

I7-3705 

29 

1.05380 

7.986 

8.415 

17.2497 

30 

1.05388 

8.064 

8.498 

17.1238 

31 

1  -°5397 

8.144 

8-583 

16.9926 

32 

.05407 

8.237 

8.681 

16.8557 

33 

.05419 

8.342 

8.794 

16.7131 

34 

•0543  * 

8.451 

8.909 

16.5646 

35 

•05443 

.8.<;6i 

,  9.027 

16.4099 

36 

•05458 

8.697 

8.172 

16.2487 

37 

•05474 

8.837 

9.320 

16.0811 

38 

•05493 

9.003 

9-497 

15.9066 

39 

-05512 

9.174 

9.679 

I5-7253 

40 

•05534 

9-373 

9.891 

15.5669 

4i 

•05556 

9-577 

10.109 

I5-34I3 

42 

•05583 

9.811 

10-359 

15.1382 

43 

.05611 

10.064 

10.629 

14.9275 

44 

1.05644 

10.363 

10.947 

14.7059 

45 

1.05680 

10.682 

11.289 

14.4826 

46 

1.05722 

11.064 

11.687 

14.2484 

47 

1.05769 

11.484 

12.146 

14.0065 

OF  LIFE   INSURANCE. 

TABLE  No.  LXVI— (CONTINUED.) 
VALUATION  COLUMNS. 


169 


AMERICAN  EXPERIENCE,  FOUR  AND  A  HALF  PER  CENT. 

Agt. 

«z 

c* 

*, 

4 

48 

1.05824 

•  11-771 

12.668 

13.7569 

49 

1,05888 

12,542 

13.280 

13.4998 

50 

1.05960 

13.188 

13-974 

13-2358 

51 

1.06042 

13.915 

14-755 

12.96151 

52 

1.06133 

14.726 

15-629 

12.6880 

53 

1.06235 

15-630 

16.604 

12.4049 

54 

1.06350 

16.6.1; 

17.704 

12.1160 

55 

1.06478 

17.771 

18.922 

11.8218 

56 

1.06020 

19.031 

20.289 

11.5228 

57 

1.06778 

20.416 

21.800 

11.2194 

58 

1.06953 

21.948 

23-474 

10.9121 

59 

1.07149 

23.656 

25-347 

10.6013 

60 

1  .07366 

25-544 

27-425 

10.2877 

61 

1.07608 

27.637 

29-739 

9.9718 

62 

1.07876 

29.949 

9-6544 

63 

1.08  72 

32.481 

35-I36 

9-3360 

64 

1.68501 

35.285 

38.285 

9.0172 

65 

1.08869 

38.401 

41.807 

8.6987 

66 

1.09276 

41.825 

45-704 

8.3814 

67 

1.09728 

45-596 

50-031 

8.0662 

68 

1.10232 

49.763 

54-855 

7.7536 

69 

1.10789 

54-318 

60.178 

7.4446 

70 

1.11406 

59-323 

66.090 

7.1399 

71 

1  .  1  2084 

64.752 

72.576 

6.8402 

72 

1.12818 

70.557 

79.602 

6.5460 

73 

1.13609 

76.725 

87-167 

6.2569 

74 

1.14461 

83.280 

95-323 

5.9723 

75 

1.15389 

90.307 

104.204 

5.6914 

76 

1.16410 

97-905 

"3-971 

5.4133 

77 

1-  '7556 

106.211 

124.941 

5-1376 

78 

1.18862 

115.621 

137-433 

4.8640 

79 

1-20355 

126.061 

1151.720 

4.5928 

So 

1.22156 

138.245 

168.861 

4.3241 

1 70 


PRINCIPLES  AND  PRACTICE 

TABLE   No.  LXVI— (CONTINUED). 
VALUATION  COLUMNS. 


AMERICAN  EXPERIENCE,  Six  PER  CENT. 

Age. 

-. 

.«. 

*, 

* 

15 
16 

1.06813 
1.06818 

7.202 

7.227 

•  7.692 
7.720 

15.1368 
15.1003 

17 

1.06821 

7-253 

7-747 

15.0617 

18 

1.06825 

7.289 

7-787 

15.0208 

19 

1.06830 

7-326 

7.826 

14.9778 

20 

1.06834 

7-363 

7.866 

I4-9325 

21 

1.06839 

7.411 

7.917 

14.8846 

22 

1.06845 

7-4S9 

7-969 

14.8342 

23 

1.06850 

7.508 

8.022 

14.7811 

24 

1.06856 

7-558 

8.076 

H-7252 

25 

1.06862 

7.608 

8.130 

14.6662 

26 

1  .06869 

7.670 

8.197 

14.6039 

27 

1.06877 

7-733 

8-265 

I4-5383 

28 

1.06882 

7-797 

8333 

14.4694 

29 

1.06892 

7-873 

8-415 

14.3964 

30 

1.06901 

7-950 

8.499 

H-3'97 

31 

1.06910 

8.029 

8-583 

14.2388 

32 

.06920 

8.120 

8.682 

14-1536 

33 

.06932 

8.224 

8-795 

14.0639 

34 

.06944 

8.331 

8.910 

13-9695 

35 

.06957 

8.440 

9.027 

13.8701 

36 

.06972 

8-  574 

9.172 

I3-7655 

37 

.06988 

8.711 

9.320 

I3-6555 

38 

.07007 

8.876 

9.498 

13-5399 

39 

.07026 

9.044 

9-679 

13-4185 

40 

I  .07048 

9.240 

9.891 

13  2911 

41 

1.07071 

9.441 

10.109 

I3-I574 

42 

1.07098 

9.672 

10-359 

13.0174 

43 

1.07127 

9.922 

10.629 

12.8701 

44 

1.07160 

10.216 

10.947 

12.7160 

45 

1.07197 

10.531 

11.289 

1  2-5549 

46 

1.97240 

10.907 

11.697 

12.3865 

47 

1.07287 

11.321 

12.146 

12.3108 

OF  LIFE  INSURANCE. 

TABLE  No.  LXVI.— CONTINUED. 
VALUATION  COLUMNS. 


171 


AMERICAN  EXPERIENCE,  Six  PER  CENT. 

Affe. 

«»• 

e,- 

**• 

Ax. 

48 

1-07343 

11.801 

12.668 

12.0278 

49 

1.07407 

12.364 

13.280 

11.8376 

50 

1.07481 

13.001 

13-974 

11.6404 

51 

1.07564 

I3-7I7 

H755 

"•4365 

52 

1.07657 

14.518 

15.629 

11.2259 

53 

1.07760 

15.409 

16.604 

11.0089 

54 

1.07877 

16.411 

17.704 

10.7859 

55 

1.08006 

17.520 

18.922 

10-5563 

56 

1.08150 

18.760 

20.289 

10.3214 

57 

1.08311 

20.128 

21.800 

10.0811 

58 

1.08488 

21.637 

23-47,4 

9-835S 

59 

1.08687 

23.321 

25-347 

9-5858 

60 

1.08907 

25.182 

27-425 

9-33I7 

61 

1.09152 

27-245 

29-739 

9-0738 

62 

1.09424 

29.520 

32.302 

8.8127 

63 

1.09725 

32.022 

35-136 

8.5490 

64 

1.10058 

34.786 

38.285 

8.2831 

65 

1.10431 

37-858 

41.807 

8.0156 

66 

1.10485 

41-233 

45-704 

7-7475 

67 

1.11303 

44-951 

50-031 

7.4792 

68 

1.11815 

49.058 

54-S54 

7.2116 

69 

1.12379 

53-549 

60.178 

6-9455 

70 

1.13006 

58.484 

66.090 

6.6815 

7i 

1.13693 

63.836 

72-576 

6.4204 

72 

1.14438 

69-559 

79.602 

6.1626 

73 

I-I5239 

75-94° 

87.167 

5-9079 

74 

1.16104 

82.102 

95-323 

5-6559 

75 

1.17046 

89.029 

104.205 

5-4057 

76 

i.iSoSi 

96.519 

113-971 

5-1567 

77 

1.19244 

104.778 

124.941 

4.9082 

78 

1.20568 

113.988 

137-433 

4.6603 

79 

1.22082 

124.277 

151.720 

4-4i3i 

80 

1.23899 

136.288 

168.861 

4.1669 

172 


PRINCIPLES  AND  PRACTICE 


TABLE  No.  LXVI— (CONTINUED.) 
VALUATION  COLUMNS. 


Age. 

COMBINED  EXPERIENCE,  FOUR  PER  CENT. 

Dx 

cx 

cx 

Ni 

A*«"  ^ 

ux 

"x+1 

JDX   A* 

15 

1.04727 

6.677 

6.992 

19.9976 

16 

1-04733 

6-733 

7.052 

19.8957 

17 

1.04740 

6.791 

7-"3 

19.7901 

18 

1-04757 

6.860 

7-185 

19.6807 

'9 

1.04755 

6.929 

7-259 

'9-5675 

20 

1.04764 

7.010 

7-344 

19.4504 

21 

1-04773 

7-093 

7-432 

I9-3293 

22 

1.04782 

7-U7 

7.520 

19.2041 

23 

1.04793 

7-273 

7.622 

18.0747 

24 

1.04803 

7.371 

7-725 

18.9410 

25 

1.04814 

7.471 

7.830 

18  8027 

26 

1.04827 

7.583 

7-949 

18.6589 

27 

1.04839 

7.698 

8.071 

18.5122 

28 

1.04854 

7.826 

8.206 

iS-3597 

29 

1.04868 

7-956 

8-344 

18.2023 

30 

1.04884 

8.101 

8.497 

18.0396 

31 

1.04900 

8.248 

8.652 

17.8718 

32 

1.04958 

8  410 

8.824 

17.6985 

33 

1.04936 

8.576 

8.999 

17.5196 

34 

*  -04955 

8746 

9.179 

I7-3350 

35 

1.04975 

8-931 

9-375 

17.1444 

36 

1.04996 

9.122 

9-576 

16.9475 

37 

1.05017 

9.3I3 

9.782 

l6-7443 

38 

1  .05040 

10.005 

16.5342 

39 

1.05064 

9741 

10.235 

16.3172 

40 

.05089 

9963 

10.470 

16.0929 

41 

.05116 

10.204 

10.726 

15.8610 

42 

.05146 

10.476 

11.014 

15.6212 

43 

•05183 

10.818 

"•379 

I5-3736 

44 

•05231 

11.247 

11.836 

15.1186 

45 

.05286 

11.742 

12.363 

14.8571 

46 

•05353 

12-345 

13.006 

14.5896 

47 

•05425 

12.996 

13.701 

14.3170 

OF  LIFE   INSURANCE. 

TABLE  No.  LXVI— (CONTINUED.) 
VALUATION  COLUMNS. 


173 


Agt. 

COMBINED  EXPERIENCE,  FOUR  PER  CENT. 

Dx 

cx 

cx 

Nx   A 

n    —  Ux 
•L/x  +  i 

*>,~c* 

D9  +  l   k* 

•Dx 

48 

1  -05504 

13-711 

14.466 

14.0394 

49 

1.05590 

14.482 

15.291 

I3-757I 

50 

1.05684 

*5-326 

16.197 

I3-4703 

5i 

1.05788 

16.248 

17-189 

13.1792 

52 

1.05901 

17-257 

18.275 

12.8841 

53 

1.06024 

iS-359 

19.464 

12.5853 

54 

1.06156 

*9-532 

20-735 

12.2832 

55 

1.06303 

20.831 

22.144 

11.9779 

56 

1.06462 

22.237 

23.674 

11.6698 

57 

1.06632 

23-730 

25-304 

"•3593 

58 

1.06819 

25-37I 

27.101 

11.0463 

59 

1.07023 

27.160 

29.068 

Io-73I3 

60 

1.07254 

29.169 

31-285 

10.4149 

61 

1.07506 

31-357 

33-7" 

10.0977 

62 

1.07786 

33-770 

36.399 

9.7805 

63 

1.08090 

36-384 

39-32S 

9.4641 

64 

1.08427 

39-255 

42-563 

9.1489 

65 

1.08796 

42.386 

46.115 

8-8355 

66 

1.09199 

45.782 

49-994 

8.5248 

67 

1.09644 

49.494 

54.268 

8.2170 

68 

I.IOI26 

53-490 

58.907 

7-9!30 

69 

1.10648 

57-776 

63.928 

7.6130 

70 

I.II222 

62.436 

69.442 

7-3I72 

7i 

I.IIS47 

67.460 

75-452 

7.0261 

7^ 

I-I2530 

72.889 

82.022 

6.7400 

73 

I-I3275 

78-734 

89.186 

6-4593 

74 

1.14093 

85.065 

97-054 

6.1840 

75 

1.14988 

91.885 

105-657 

5.9146 

76 

I-I5965 

99.211 

115.050 

5-6512 

77 

I.I7047 

107.182 

125-453 

53-938 

78 

1.18242 

115.812 

136.938 

5.1428 

I9 

I.I9549 

125.062 

149.511 

4.8986 

80 

1.20087 

135.006 

163.340 

4.6607 

INDEX. 


PACK 

Accumulation  formula,  Wright's 150 

"  "          Fackler's 150 

"  "          McClintock's 144 

American  Experience  Mortality  Table 33.  68 

' '        Commutation  Columns,  4  %  per  cent 70 

"        Commutation  columns,  6  per  cent , 74 

Annuities  Certain,  At  Compound  Interest 19 

1 '         Deferred 23 

"         Formulae  for 143. 

' '         Life 43 

Average  Duration  of  Policies 66 

Combined  Experience  or  Actuaries  Table  of  Mortality^ 34,  69,  98 

"          Experience  Commutation  Columns,  4  per  cent 72 

Commutation  Columns,  How  Made 36' 

Contribution  Explained  .• 50 

Formulae,  Homans's 151 

Cost  of  Insurance  Explained 48,  120 

Single  Premium,  Whole  Life  Policy,  American  Experience, 

4%  per  cent 121 

"  Combined  Experience, 

4  per  cent 121 

"  Whole  Life  Policy,  American  Experience,  4^  per  cent 122 

"  Ten  Payment  Life  "  "  123 

"  Ten  Year  Endowment  "  "  124 

"  Fifteen  Year  Endowment        "  "  125 

"  Twenty  Year  Endowment      "  "  126 

"  Twenty-five  Year  Endowm't "  "  127 

"  Thirty  Year  Endowment        "  "  128 

"  Whole  Life  Policy,  Combined  Experience,  4  per  cent 129 

"  Ten  Payment  Life  "  "  130 

"  Ten  Year  Endowment  "  -"  131 

"  Fifteen  Year  Endowment  "  "  132 

Twenty  Year  Endowment          "  "  133 

Twenty-five  Year  Endowment  "  134 

Thirty  Year  Endowment  "  "  135 

Decimal  Parts  of  a  Year,  to  January  ist  following 140 

Definitions n 

Discount 21 

Endowment,  Simple 42 

' '  Insurance 43 

"  Insurance,  Formulae  for 144,  146 


INDEX.  ^5 

PAGK 

Equation  of  Life 57 

"      Table  of 58 

"      Formulas  for 151 

Expectation  of  Life 55 

Table  of 56 

"            Not  Adapted  to  Determine  Premiums 57 

Formulas  for 151 

Forfeiture  of  Policies  and  Paid-up  Insurance 62 

Formulae  for  Verifying  Commutation  Columns 151 

Gross  Valuation 46 

Insurance  Paid-up 62 

1 '          Term 42 

' '          Values,  Mr.  Wright's  Formulae  for 151 

Interest 16 

"     Compound 16 

' '     Rate  of 34 

Joint  Life  Policies 59 

' '                 Valuation  of  Chandler's  Method 156 

"                 Valuation  of  Chandler's  Table  for 157 

' '                  Formulae  for 146 

Life  Contingencies 32 

Life  Insurance,  Explanation  of 37 

1 '            Formulas 142' 

Massachusetts  Non-Forfeiture  Law. 63 

"                           "                    Net  Single  Premiums  Applied  -to 130 

"  ...    "  Insurance  on  Lapsed  Whole  Life  Policies, 

According  to 136 

Monetary  Tables,  4    per  cent 24 

4^  "       25 

5  "       26 

"               6  "       27 

"               7  "       28 

"               8  "       29 

9          "       3° 

10          "       31 

Mortality,  Tables  of 33 

Mortality  Table,  American  Experience  Table 68 

' '             Combined  Experience 69 

Net  Premiums  American  Experience,  4^  per  cent 76 

"              Combined  Experience,  4,  per  cent 77 

"              Joint-Lives,  Combined  Experience 114 

"              Term  Insurance,  American  Experience,  4^  percent 78 

"              Term  Insurance,  Combined  Experience,  4  per  cent 78 

Net  Valuation 46.  8o 

Net  Values,  Whole  Life  Policies,  American  Experience,  4^  per  cent. .    82 

' '            Ten  Payment  Life                       "                                           84 

"            Ten  Year  Endowment                "                                            86 

"            Fifteen  Year  Endowment                                                        88 

"            Twenty  Year  Endowment         "                                            ....:....  90 

"            Twenty-five  Year  Endowm'nt   "                           "               92 

"            Thirty  Year  Endowment            "                           "               94 

"            Thirty  five  Year  Endowment    "                           "               96 


!^6  INDEX. 

PAGE 

Net  Values,  Whole  Life  Policies,  Combined  Experience,  4  per  cent ico 

1 '  Ten  Payment  Life  "  "  102 

"  Ten  Year  Endowment  "  "  104 

"  Fifteen  Year  Endowment  "  "  106 

' '  Twenty  Year  Endowment         "  "  108 

"  Twenty-five  Year  Endowment  "  "  no 

"  Thirty  Year  Endowment  "  "  112 

"  Joint  Life  Policies,  Equal  Ages  "  115 

"  "  Diiference  in  Ages,  5  Years  "  116 

"  "  "  10  Years"  117 

IS  Years  "  118 

Premiums,  Life,  Explained 38 

Present  Values 21 

Probability  of  Life 35 

Return  Premium  Plan 60 

' '  Formulae  for 147 

"  Loaded  Annual  Premiums,  Formulas  for 147 

"  Net  Annual  Premium  for  Return   of  Gross  Premiums, 

Formulas  for 147 

' '  Limited  Payment 148 

Single  Return  Premium 148 

' '  Loaded  Return  Premium 148 

Return  Premiums,  Disadvantage  of,  Illustrated 61 

Risk,  Amount  at 47 

Surplus,  Distribution  of 49 

"  Formulas  for,  Roman's 151 

Surrender  Values 64 

"  Prof.  Bartlett's  Formulas  for 152 

Tables  of 155 

Sinking  Fund,  see  Monetary  Tables. 

Term  Insurance,  Formulae  for 144,  146 

"  Net  Premiums 78 

Tontines,  and  Tontine  Dividends 53 

Valuation  Tables,  American  Experience,  4}^  per  cent 168 

"  "  6          " 170 

"  Combined  Experience  4          "         172 

Valuation  of  Policies,  Net  and  Gross 45,  148 

'  McClintock's  Method 158 

Whole  Life  Policy,  Formulas  for 144,  146 


V 


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